Was Snow turning senile?

TLDR:

I don't believe he was senile. I believe overwhelming anger amongst the districts, coupled with District 13, coupled with a meaningful figurehead, presented a rebellion so large even his intelligence and cunning wasn't enough to defeat it.

(Very, very) long Answer:

I'll confess, I don't have a word of god interview. It appears Suzanne Collins doesn't give too many interviews. There are quite a few where she discusses Catching Fire, but I've yet to find anything meaningful where she discusses Mockingjay and the role of President Snow.

Despite this, I'm going to try to answer this based on the books, looking at The Hunger Games and Snow’s behaviour throughout:

The Hunger Games novel

In Chapter 1 of the Hunger Games, we are told:

…Then came the Dark Days, the uprising of the districts against the Capitol. Twelve were defeated, the thirteenth obliterated. The Treaty of Treason gave us the new laws to guarantee peace and, as our yearly reminder that the Dark Days must never be repeated, it gave us the Hunger Games.

The rules of the Hunger Games are simple. In punishment for the uprising, each of the twelve districts must provide one girl and one boy, called tributes, to participate. The twenty four tributes will be imprisoned in a vast outdoor arena that could hold anything from a burning desert to a frozen wasteland. Over a period of several weeks, the competitors must fight to the death. The last tribute standing wins.

…

Whatever words they use, the real message is clear. “Look how we take your children and sacrifice them and there’s nothing you can do. If you lift a finger, we will destroy every last one of you. Just as we did in District Thirteen.”

I've highlighted a few sections for effect. Now, I don't believe it’s ever stated how long Snow is in charge of the Capitol for (and his age of 76 on the wiki isn't cited). However, I think it's fair to say he wasn't the creator of the Hunger Games - but he's still obviously overseen at least a few of the games (we know he was president during the 50th quell when Haymitch won).

So at this point in the novel, we know he's inherited a rather barbaric and twisted method of controlling the population of the Twelve Districts. And up until now, it appears he's done this very successfully.

Catching Fire novel

In the opening chapter, Snow visits Katniss and we read the following exchange:

“I have a problem, Miss Everdeen,” says President Snow. “A problem that began the moment you pulled out those poisonous berries in the arena.”

That was the moment when I guessed that if the Gamemakers had to choose between watching Peeta and me commit suicide—which would mean having no victor— and letting us both live, they would take the latter.

“If the Head Gamemaker, Seneca Crane, had had any brains, he'd have blown you to dust right then. But he had an unfortunate sentimental streak. So here you are. Can you guess where he is?” he asks.

So Snow clearly recognised the danger of their actions right away and would have happily killed both of them. He would have infuriated the 12th district, but clearly he was confident in being able to quell any dissatisfaction.

However, Seneca chose to keep them alive and, after being announced as the winners, Snow had to crown them (although as the previous quote shows, he did it with hated). He recognised at that stage what a threat Katniss could be and that it was a mistake to let her live.

Of course, the problem from Snow's view is simple:

“...You have no access to information about the mood in other districts. In several of them, however, people viewed your little trick with the berries as an act of defiance, not an act of love. And if a girl from District Twelve of all places can defy the Capitol and walk away unharmed, what is to stop them from doing the same?” he says. “What is to prevent, say, an uprising?”

So he's clearly concerned all ready. So why not just kill Katniss now? That is discussed as well:

“Why don't you just kill me now?” I blurt out.
“Publicly?” he asks. “That would only add fuel to the flames.”
“Arrange an accident, then,” I say.
“Who would buy it?” he asks. “Not you, if you were watching.”

So at this stage his reasoning is clear. He cannot kill Katniss, for fear of sparking a rebellion - but her very act of being risks sparking a rebellion as well.

Given this, Snow feels his only option is to convince her to help suppress the rebellions:

“Only you'll have to do even better if the uprisings are to be averted,” he says. “This tour will be your only chance to turn things around.”

“I know. I will. I'll convince everyone in the districts that I wasn't defying the Capitol, that I was crazy with love,” I say.

President Snow rises and dabs his puffy lips with a napkin. “Aim higher in case you fall short.”

“What do you mean? How can I aim higher?” I ask.

“Convince me” he says.

So his initial plan is very clear - make sure she helps him suppress any rebellious notions. And given what we've heard, it seems reasonable. He's concerned about killing her, he can't have her "disappear" and he's concerned about letting her speak her mind. His only realistic option is to get her "on board" with his plans.

Of course, this doesn't go quite to plan...

My voice is undependable, but I am almost finished. “Thank you for your children.” I raise my chin to address the crowd. “And thank you all for the bread.”

I stand there, feeling broken and small, thousands of eyes trained on me. There's a long pause. Then, from somewhere in the crowd, someone whistles Rue's four-note mocking-jay tune. The one that signaled the end of the workday in the orchards. The one that meant safety in the arena. By the end of the tune, I have found the whistler, a wizened old man in a faded red shirt and overalls. His eyes meet mine.

What happens next is not an accident. It is too well executed to be spontaneous, because it happens in complete unison. Every person in the crowd presses the three middle fingers of their left hand against their lips and extends them to me. It's our sign from District 12, the last good-bye I gave Rue in the arena.

If I hadn't spoken to President Snow, this gesture might move me to tears. But with his recent orders to calm the districts fresh in my ears, it fills me with dread. What will he think of this very public salute to the girl who defied the Capitol?

The full impact of what I've done hits me. It was not intentional—I only meant to express my thanks — but I have elicited something dangerous. An act of dissent from the people of District 11. This is exactly the kind of thing I am supposed to be defusing!

So although Katniss has just stirred up a rebellion, exactly what was to be avoided, she did it unintentionally. Snow's plan, to an extent, was working. Katniss is terrified. But through pure naivety, she has done what she was meant to avoid.

To try and dampen this, Snow suppresses the footage of this small rebellion and gives them pre-written speeches:

Even without our personal speeches to trigger dissent— needless to say the ones we gave in District 11 were edited out before the event was broadcast—you can feel something in the air, the rolling boil of a pot about to run over. Not everywhere. Some crowds have the wearycattle feel that I know District 12 usually projects at the victors' ceremonies. But in others — particularly 8, 4, and 3 — there is genuine elation in the faces of the people at the sight of us, and under the elation, fury. When they chant my name, it is more of a cry for vengeance than a cheer.

So Snow is already becoming increasing trapped. Katniss is becoming a dangerous symbol. However, his possible actions are limited. Her (unintentional) actions above clearly aggravate him, but he’s stuck as to how to move against her. Realising this, Katniss wants Gale, Peeta and their families to run. She is terrified and fearing for her life:

“Peeta, if I asked you to run away from the district with me, would you?”

Peeta takes my arm, bringing me to a stop. He doesn't need to check my face to see if I'm serious.

"Depends on why you're asking.” “President Snow wasn't convinced by me. There's an uprising in District Eight. We have to get out,” I say.

Katniss however begins to realise just how scared Snow is:

Listening to Bonnie and Twill confirmed one thing: President Snow has been playing me for a fool. All the kisses and endearments in the world couldn't have derailed the momentum building up in District 8. Yes, my holding out the berries had been the spark, but I had no way to control the fire. He must have known that. So why visit my home, why order me to persuade the crowd of my love for Peeta?

It was obviously a ploy to distract me and keep me from doing anything else inflammatory in the districts. And to entertain the people in the Capitol, of course. I suppose the wedding is just a necessary extension of that.

So Katniss has begun to realise that Snow has to keep her under control. Snow, meanwhile, wants to rapidly defuse the situation in the districts. To do this, he unleashes a plan. Every year, the Hunger Games provides entertainment and fascination across all the districts. So he decides to put on a special Hunger Games involving former winners, including Katniss.

So with one fell swoop, Snow is hoping to both have Katniss killed in the one place her death would not be suspicious and to defuse the situation in the districts by providing entertainment - and reminding them of how powerless they are in the face of the Capitol's power. This isn't particularly illogical.

However, before entering the games both Katniss and Peeta both do something that's not expected:

Wonderingly, I lift my long, flowing sleeves into the air, and that's when I see myself on the television screen. Clothed in black except for the white patches on my sleeves. Or should I say my wings.

Because Cinna has turned me into a mockingjay.

First, an incredible, rebellious transformation. And then:

…“We're already married,” says Peeta quietly. The crowd reacts in astonishment, and I have to bury my face in the folds of my skirt so they can't see my confusion. Where on earth is he going with this?

...

...This takes even Caesar aback. “Surely even a brief time is better than no time?”

“Maybe I'd think that, too, Caesar,” says Peeta bitterly, “if it weren't for the baby.”

Suddenly, they're no longer playing Snow's game. They're directly rebelling. This leads to something truly extraordinary:

And then it happens. Up and down the row, the victors begin to join hands. Some right away, like the morphlings, or Wiress and Beetee. Others unsure but caught up in the demands of those around them, like Brutus and Enobaria. By the time the anthem plays its final strains, all twenty-four of us stand in one unbroken line in what must be the first public show of unity among the districts since the Dark Days. You can see the realization of this as the screens begin to pop into blackness. It's too late, though. In the confusion they didn't cut us off in time. Everyone has seen.

Now, this really has sparked off the rebellion. Snow wasn’t expecting this, and given the threats levied against Katniss it’s understandable that he wasn’t expecting it.

Of course, following this something happens that is simply a massive, war-losing mistake on Snow's part - he doesn't realise Plutarch Heavensbee is an insider, working for the rebellion. He schedules the Games to rid himself of Katniss and try to defuse the districts. Instead, a collection of victors - potential figureheads for the rebellion - escapes and a full war, driven by District 13 as well - breaks out.

But again, I’m not sure this makes him senile. It’s an oversight, sure, but plenty of intelligent, crafty people have been fooled.

Mockingjay

All of this means that when we reach the Mockingjay novel, all pretences have been left behind and Snow and Katniss are finally out to truly kill each other. The very opening chapter of the book shows this, when Snow leaves the white rose in her house in District 12.

But it’s not as simple as crushing the rebels:

Their early years must have been terrible, huddled in the chambers beneath the ground after their city was bombed to dust. Population decimated, no possible ally to turn to for aid. Over the past seventy-five years, they've learned to be self-sufficient, turned their citizens into an army, and built a new society with no help from anyone. They would be even more powerful if that pox epidemic hadn't flattened their birthrate and made them so desperate for a new gene pool and breeders. Maybe they are militaristic, overly programmed, and somewhat lacking in a sense of humor. They're here. And willing to take on the Capitol.

District 13, which is spearheading this rebellion, is a militaristic group. And there is a sizable amount of dissent in the various districts. Snow can feel control slipping away.

His next decision is again quite logical - he tries to use Peeta to force a ceasefire through. Of course, the District 13 rebels including Katniss don't believe this. But Snow is also hoping to convince the many other rebels, who are not part of District 13's army, of downing their weapons. Of course, it doesn't work.

Snow sends a bombing campaign to District 13 - but the rebels are underground in their bunkers, and escape fairly unscathed. Snow does leave white roses to symbolise his presence and attempt to threaten them, but this has not, and will not, suppress the fighting.

Snow even sends Peeta back to her, brainwashed, in an attempt to both physically harm her or psychologically damage her - but again, it is to no avail.

And from this point on, Snow is on the defensive, gradually being beaten back until his eventual defeat.

Conclusion:

I strongly believe Snow was a ruthless, but highly intelligent leader who faced an inevitable rebellion which he simply could not control.

He wanted Katniss dead from the very moment of her first rebellion. He was intelligent enough to see her danger, but was powerless to kill her after she won the Games.

Rather than risk her becoming a martyr, her kept her alive and "on-side". This failed spectacularly, despite her attempts to please him - the rebellion gained traction.

Finally, he decides to kill her, but via the Games to both remove her, provide some form of entertainment in the districts and to remind the districts of their powerlessness.

This falls apart because of the "inside" Plutarch.

This leads Snow and the rebels into an all out war - but District 13 is well prepared, militaristic and has a bunker where the bombings don't affect them. Coupled with this is an angry, nothing-to-lose population across all the suppressed districts, who have finally found a figurehead to be their guiding light in a rebellion.

The combination of all these factors was too much for even the ruthless Snow, and he was defeated.

But none of this makes him senile. Instead, I would postulate that his actions were extremely intelligent and calculated, but that he was extremely limited in his options. From the moment Katniss (and Peeta) won the Hunger Games, dissent began to brew and a number of factors (including the strength of the combined districts and ferocity of the rebels) contributed to his (and the Capitol's defeat). This echoes history and a number of instances of powerful empires (Greeks, Egyptians, and particularly The Romans - whom the Capitol in the book were partly modelled - and their defeats).

So again, I don't think he's senile - I believe he was simply on the receiving end of a string of concatenated events over which even the mighty Capitol couldn't maintain control.