I first developed this theory and made a thread about it several months before the finale. After watching the finale, I feel that it has been more or less confirmed. It basically concerns a common pattern that I believe lies behind all of Azula's non-victories, at least as far as combat is concerned.

I've been re-watching Avatar, and I've noticed something about Azula, or, more specifically, about the fights she's in, and how her enemies somehow manage to keep surviving her. Every time she has outmaneuvered and/or beaten her opponents, has them at her mercy, and is able to move in for the kill, she always hesitates for some reason, holding back to savor her triumph, and her enemies take adavtage of this, and Azula either does not achieve her goal, or comes off worse in the fight. Every single Azula fight in the series where she hasn't won has ended this way. There were only two exceptions: Return to Omashu, and The Southern Raiders. Here are some examples:

- In The Avatar State, Azula easily defeats Zuko. But after she has knocked him out, instead of shooting a quick fireball at him and killing him, she takes her time generating a gigantic lightning bolt, no doubt wishing to show off her new skills. Iroh then appears and kicks her off the boat.

You must remember though that Azula is precise, not wild and violent (at this point in the story ;p). Using lightning to kill Zuko not only follows her personal philosophy of precision and coldbloodedness but is also an actual "one hit kill" move. Yes, she could shoot a fireball at him and while that would severely injure him (unless the salvo was continued) but lightning is a guaranteed kill that. One could look at it this way. Fire is for fighting, lightning is for killing, if that makes sense.

- After defeating Aang and Zuko in The Chase, Azula had a moment when she could easily have killed Aang, who was trapped under a pile of burning wood. Instead, she simply stood there smiling, probable thinking about the best way to torture him to death. Suddenly, Katara, Sokka, Toph, and Iroh had all appeared out of nowhere, Zuko had woken up, and she was forced to flee. She did pretty much the same thing in The Drill after she had defeated Aang, and in the moment she hesitated, Aang woke up and was able to continue the fight.

She did stand there smiling but not because she was thinking of torturing him (even though that's easy to believe). I have no doubt in my mind that she was savoring the moment of seeing the Avatar trapped and at her mercy. Once again, we see her getting her fingers ready for lightning. Once again, wildy shooting fire at him for the kill is not her and while she could have done that, she was still enjoying her victory. She was a couple of seconds away from victory but the bad timing of the arrival of all of her enemies at once is what defeated her. Same goes for The Drill. She saw that he was down, despite being ready to attack, but wanted to enjoy it rather than just fire away.

- When capturing Zuko and Iroh in The Crossroads of Destiny, the smart thing for Azula to do would have been to get the Dai Lee to simply collapse the walls of the tea room and bring the roof down on them, or at least get the Dai Lee to do it without her. Instead, unable to resist the urge to show off, she walked in and revealed herself, and as a result Iroh escaped and almost ruined everything for her by fetching Aang, Sokka, and Toph.

She revealed herself because she believed she had them surrounded, captured and that was apparently her objective at that point. Like earlier too, she was being smug about it all. Besides, it turns out Zuko was in her plans afterall.

- After her victory in The Day of Black Sun, Azula didn't bother to have anyone try to follow Appa. Even though one of the war balloons wouldn't have been able to catch up with Appa, an attempt at pursuit would probably have caught Zuko, and eventually have lead to the Western Air Temple. Instead, Zuko was able to meet up with the Aang and become his firebending master, which of course wouldultimately lose the Fire nation the war.

It followed her philosophy. Why chase them down (when they are faster) when you know they'll come to you? Rather than go on a wild goose chase, she was most likely going to patiently wait it out until they returned.

- She does it again in the final fight of The Boiling Rock; Part 2. Once she had safely flown to another cable car, the smart thing for Azula to do would have been to shoot a lightning bolt at the other cable car, ending the fight. Instead, wanting to watch it fall into the lake and listen to Zuko's screams as he was boiled to death, she was content to wait for the guards to cut the line, and by the time she realised that Mai had betrayed her and stopped them, it was out of range and the gaang were able to escape.

It's basically the same situation as The Drill and The Chase. She doesn't just wildy launch attacks for the sake of destroying. Again, she wanted to enjoy the sight, watching Zuko fall finally fall to his death.

- The writers continue this in the finale, with the way Azula is finally brought down After she has beaten Zuko (come on, admit it - Zuko got pwned once again), Azula chases Katara around and eventually manages to corner her. Azula could easily have killed Katara at this point. The drain that Katara was hoping Azula would step on was still several meters in front of her, Katara was directly ahead, with no defence against the fire blasts Azula could have summoned up with Sozin's comet overhead - basically as good as dead. And yet Azula did not fire. Instead she fired off a couple of final insults, had a brief staring competition with her, and then walked towards her over the drain, and was consequently frozen and chained up.

Yeah, with the power of the comet she could have easily just vaporized her from afar. Even sane Azula would have done that. :p That had to be the mania talking but she still probably wanted to kill Katara up close to enjoy it... Especially if one is manic. Wether or not that was Katara playing on her weakness (Azula coming after her rather than just shooting her from afar) or was simply chance that Azula walked over the grate, I don't know. But what is certain though is that her mental state was affecting her in that fight, primarily her mania.

There are several possible explanations for this apparent weakness in Azula's fighting. The first, and most obvious, is that it was simply a writing tool; obviously Azula couldn't kill her enemies, or the story would be over. Cue the deus ex machina. However, I don't think that this is very likely. If all that was motivating the writers was the need to keep Azula's enemies alive, they would have varied from the formula of having Azula's enemies at her mercy, having her hesitate, and then having said enemies take advantage of this and escape/win. At times, it borders on the blatantly obvious: the manner in which Aang escaped her in "The Chase" and "The Drill" was so bizarrely similar, that it was this that first lead me to my suspicion that there was a pattern behind Azula's defeats. This would imply that the writers wanted to develop this as an established weakness of Azula's - setting a precedent, if you will, for how the epitome of perfection is eventually defeated. The outcome of the Agni Kai in the finale was what clinched this theory for me: AKA; Azula having Katara at more or less point blank range, and yet still insisting on drawing out the kill. Granted, she was not herself at the time - the Azula we all know and love would never have been caught dead standing around monologuing when she had a perfect opportunity to finish off her foe. But still, it fits with the above mentioned examples.

I will agree with you on that again. The smart thing for the sane Azula to do would have been to attack her from afar but that wasn't the case due to her mental state. So, if you look at it like that, it renders the idea of her "weakness" being taking a moment to pride herself before the kill since if she was in a right state of mind she would hae gone all out on Katara anyway.

Discuss this theory, and add to or disagree with it if you wish.

EDIT: I do not have a theory behind the exact reasoning for Azula's frequent willingness to hold back. Sometimes it seems to be because she wants to show off (The Avatar State). Sometimes it seems to be because she is supremely confident (DoBS). Perhaps there is a deeper meaning. That is what I am hoping people will discuss.