Why can't Dracula save Mirena from falling even with supernatural powers?

Even if, somewhat objectively, it seems like an absurd, logical plothole in the film -- since, just as you said, he had just defeated an entire, trained army in a matter of a few minutes -- this is more of an abstract emotional, philosophical experience within the narrative of the film.

For all his powers, Dracula was borne of rage and pride. He wanted to go defeat the monster in the caves, and instead was turned into a monster. But, his monstrosity gave him the power, the raw power, to protect his kingdom and his home.

Abstractly, it's a reflection on nationalism and pride; the sense that one's kingdom comes above all else and all others. Instead of diplomacy or fleeing with his wife and child, Dracula used his powers to hold onto his castle and his kingdom, so that he would never have to run, hide, or bow-down to anyone.

While it may be a logical plothole, I believe it's meant as a lesson to Dracula. For all his strength and pride and powers, he chose to use them for defending his kingdom, not necessarily for protecting his loved ones. Because, really, he defended the physical castle, itself, from being attacked by the army. But while he's off fighting and flying and transforming, he's abandoned his family and they're just as weak and exposed and uncared-for as if he'd run off to another kingdom to invade or defend for someone else. In a very real sense, though he's only ever a few hundred feet away, he has abandoned his family.

When she is falling to her death, for all his magic and might, there are physical limitations to how fast he can fly and how far he can reach. Wildly thrashing through an army takes less focus and control than precisely timing his flight to be able to catch her and prevent her death. More abstractly, he clearly has might but he disorganized his priorities. He didn't watch over his family, he violently "defended" his castle and his kingdom. This leaves him with the dramatic irony of having successfully defend a physical home that will now forever be an empty, family-less home.

It's a nod to the concept that a house is not necessarily a home -- meaning that where you live is not always as important as how you live and who you live with.

Dracula was given power and he chose to use it for might, rather than to reflect on his circumstances, weigh his options, cherish his loved-ones, and make decisions that protect what he truly, really cares about.

The ending of the film suggests that perhaps he has a second chance, but has he truly learned from his past, or has he stewed in his rage and sorrow and not really taken ownership for his misprioritization and his own flaws and failures. Her death was not necessarily his fault, but wouldn't she still be alive if they had abandoned their castle, or given in to the other kingdom, or if he simply prioritized his family above his landscape and physical possessions?

Was her death a logical incongruity? From certain viewpoints: sure. It seems that there's an incomparable set of limitations between his powers from scene to scene.

However, as a narrative element, as a rational and logical element of the consequences of his choices, and as circumstances in the limitations of the physical world there seems to be a very blunt and obvious difference between the lateral motions of his thudding destruction against the standing army, and the vertical motion of his attempt to overcome the physical limits of gravity and velocity to prevent a death of a loved one whom he left in a blindspot out of his own pride and rage and self-righteousness. Even with great power, there a limits and more importantly there are consequences. Her death is the result of circumstance and a causality that could have been prevented, but its saving was never truly prioritized.

I would say that it's not illogical. It seems like a circumstantial cost, and, like much of the film's narrative, it deepens the humanity of Dracula in the sense of focusing on exemplifying that choices have consequences, and there are no powers, otherwordly or otherwise, that can overcome consequence.

[Note, as an aside, we should also be careful in "overpraising" this narrative as aimed at Dracula's "humanization", as this is very much a one-dimensional objectification and sadistic moralization of the otherwise-should-have-been-inherent personhood of his wife, because it's not entirely humanizing to contextualize one person's emotional journey while treating all other persons as objects of choice in their path. She was her own person with her own dreams and powers and experiences and future, and that's always a sticking point in these kinds of narratives that keeps them from being truly elevated conceptually beyond their surface elements. I think there is a lot of deep meaning here, but it's also very very muddy to reflect solely upon Dracula's experience, while every other "person" in his life is treated barely better than emotionally-conducive furniture.]