Why did Arya refuse to end it?

There are a few interpretations of this scene.

She may have bonded with him more, but he was still a monster to her. He was one of the names she recited at night, ensuring she never forgot him or his atrocious crimes. He killed the little butcher's boy she played with all the way back in Season 1. By being so close to Joffrey, he was also "part" of what brought her father Ned to his death. So despite becoming closer to him, she wasn't going to do him any favours and grant him mercy. She was going to leave him to his slow, painful death as retribution for all his actions.

Another interpretation is that it truly was mercy. She may have left him there, but unless you see someone die in Game of Thrones, you never truly know how they end up. She may have felt that after everything he did for her, killing him was a step too far and was too difficult.

Finally, you might be interested in what Maisie Williams, the actress who plays Arya, had to say about the event:

Describe what it was like to shoot the scene in the finale where Arya walks away from the wounded Hound.

It was one of my most enjoyable scenes, which sounds awful, because it’s such a deep, twisted scene. But I’m really happy with the outcome. It felt like we were all on the same page. I read the scene for so long, but then to hear Rory [McCann]—the Hound—screaming to come back and kill him, it really got to me. It’s just acting, but there’s so much of you in the character, so it’s awful to walk away from a full-grown man screaming to come back. He had all this makeup on, and broken bones and big bites on his neck. For a second, you have to remind yourself that it’s fake, because it gets intense. You have to take a breath and remember you’re not that cold-hearted bitch anymore.

How did you play her emotional state as she walked away?

I really don’t think it was spiteful. She doesn’t purposefully leave him there to die. He’s bossed her around for so long, it’s like that final straw of, “Now you take me seriously, and it’s too late.” Her whole life, she’s been desperate to prove to people what she’s capable of. Now the Hound really gets it, and it’s too late. He has almost created a monster and it’s started to backfire on him. That’s a lot for her to deal with as well. She kind of likes him! He really helped her out, and as much as it would be doing him a favor, I don’t think she wants to kill him at all. And possibly walking away is killing him. But in “Game of Thrones,” unless you’ve got a dagger in your heart, it doesn’t necessarily mean you’re dead.

And how ironic that she takes his money.

It symbolizes that moment [in episode 3] when he took the father’s silver. In that moment, she’s saying what the Hound said then: “Dead men don’t need silver.” All the lessons he taught her she’s now using against him.

As much as fans root for her, they also have a soft spot for the Hound.

Exactly. This whole season, I’ve been saying that Arya makes some decisions that people might not like. She’s very different to the person that people fell in love with in season 1. I hope that people would root for Arya, but people have learned a lot about who the Hound is and his past.

I've emboldened part of her comments, to make it clearer.

On a final note, here is some additional, spoilerific book information:

In the book, Brienne is nowhere around in this scene. The Hound fights Polliver and the Tickler (two of his brother's men) and, despite being both drunk and starving, manages to kill both of them. However, he is wounded mortally in the process. Arya won't give him mercy and leaves him to die under a tree.

Now, whilst the above is what happens in the books, the following is also interesting to note:

Brienne learns that the Hound may have made off with Sansa Stark. Following this lead, she eventually ends up at a monastery on the Quiet Isle, where she meets an Elder Brother who informs her it was the other Stark girl he had - Arya. He claims there is no chance the Hound is alive, as he buried him personally.

In this scene, the following is said:

"I know a little of this man Sandor Clegane. He was prince Joffrey's sworn shield for many a year, and even here we would hear tell of his deeds, both good and ill. If even half of what we heard was true This was a bitter, tormented soul, a sinner who mocked both gods and men. He served, but found no pride in service. He fought, but took no joy in victory. He drank, to drown his pain in a sea of wine. He did not love, nor was he loved himself. It was hate that drove him. Though he committed many sins, he never sought forgiveness. Where other men dream of love, or wealth, or glory, this man Sandor Clegane dreamed of slaying his own brother, a sin so terrible it makes me shudder just to speak of it. Yet that was the bread that nourished him, the fuel that kept his fires burning. Ignoble as it was the hope of seeing his brother's blood upon his blade was all this sad and angry creature lived for...and even that was taken away when Prince Oberyn of Dorne stabbed Ser Gregor with a poisoned spear."

As a result of this scene:

Many fans of the book believe his comments indicate the Hound still lives. In fact, many believe he is the novice gravedigger on the isle. There are quite a few clues behind this (see here), but ultimately it goes to show what I've already mentioned - unless you actually see someone die in GoT, anything is possible!

What? Kill him and let him off the hook so easily!

Arya has spent most, if not all her waking moments repeating and thinking of the names who have wronged her and the people she knew. Her family as she knows is dead. The only reason she lives and trains herself is so that she can make those people answer for their sins.

The Hound is one of those she hates. Aye, they have been on the road together for quite a while now but they are together mostly because one wants something from the other. The Hound is looking for somebody who would pay him a handsome ransom for Arya, and she is tagging along for safety. There's absolutely no love lost between the two.

Arya does not kill him because he wants to end this suffering, whereas she, wants him to suffer. She sees this as her retribution. He is finally answering for his sins. Killing him would let him escape this agony. It would be an act of mercy, something she belives the Hound does not deserve. As a final and parting kick to the teeth, she takes his gold. An act endorsed by the Hound, in which he now ironically finds himself at the receiving end.

Based on events in Season 5 episode 6, "Unbowed, Unbent, Unbroken", I'd argue that part of why she didn't kill him is that she really cares for him as a role model.

When she's playing the "Game of Faces" with Jaqen where she must tell the truth or lie convincingly (the latter of which she's not capable of), Jaquen asks her repeatedly if she hates the Hound and she says that she does but he tells her that she's lying repeatedly, giving us the insight that she's also lying to herself because she believes that she hates him.

Her actions now become clear to some point. Deep inside, much as she doesn't want to give up her identity and become "No One", she also likes The Hound.

Here's a synopsis of the conversation from an episode recap on EW.

Arya asks to play the “Game of Faces” with her moody nameless roommate. This is a game where you tell things about yourself to another person and if they can tell that you’re lying then they get to hit you with a stick. It sounds wretched, but it’s still more fun than Frisbee Golf. Later Jaqen H’ghar tests her. Arya tries to tell her story while inserting little lies, but Jaqen can always tell when she fibs. Most interestingly, her claim of hating The Hound was a lie. Also not true: Arya saying she wants to be No One. Of course she doesn’t. She’s Arya Stark. She wants super-assassin abilities, but the reason she wants these powers is for vengeance. If she fully gives up her identity as Arya, then what is the point?

According to season 6 episode 3 Arya confessed that a part of her did not want the Hound to die. She had taken him off her list.

In Season 5, while playing the faceless game with Jaqen H'ghar, Arya says she hated The Hound and left him to die. He punishes her because he thinks she is lying. She was.

Over the time she journeyed with The Hound, we got to listen to his side and we start to sympathise with him along with her...Remember, She even rejected the help of Brienne of Tarth.

GoT characters make decisions that make us see a different light of that character. During the Journey to Eyrie with The Hound, she killed men, making us question, maybe she is becoming more of a monster...more like the Hound. But what we fail to notice is she didn't kill him because she is NOT a killer. She just wants to avenge her family. And to her he no longer needed to be in the list.

To many leaving him there can be perceived as cruel but to her it was letting him live, it was giving him mercy because killing him is no longer her goal.

Let's not forget Arya is Cat's daughter. Look how horribly Cat treated Jon Snow even though he was completely blameless. And Tyrion - he saved Cat's life but she still stuck to her conviction that he'd tried to kill her son. I actually think there's a fairly strong theme in GOT of women making stupid decisions based on their emotions instead of logic. Daenerys is another example - raising hell about her husband's soldiers attacking a town to get ships and crew (she knew perfectly well how they did things), then insisting on some strange woman treating her husband, against all her tribe's advice. Even Shae, refusing to pay attention when told she was in danger. Of course, there's no lack of bad decisions in GOT, but the really incomprehensibly bad decisions seem to be made by women.