Jigoku Shojo/WMG

Ai's victims get one chance to save themselves.
When a contractor pulls the string, Ai's agents torment the victim in some appropriate manner, but it always seems to end the same way: they ask the victim if he has anything to say for himself. The victim always responds with defiance, and only then does Ai send him to Hell. So what happens if a victim does repent? We've never seen this happen, despite how horrific the torture sequences are (maybe they're magically designed to be scary but not interfere with the victim's honest response). But the agents almost always ask, so surely the answer makes a difference.
 * Just one flaw here: the people who get sent to hell for no fault of their own almost never get a torment scene, implying that they're just taken and that's it.
 * It's actually plausible if you take in consideration that she gives her victims one last chance to repent for the sin that caused the contractor to pull the string. If the contractor pulled the string out of pure spite, then the victim has no chance to repent for any sin because they are not guilty of anything, yet the sin is being pushed onto them by the contractor, so they'll invariably go to hell by the lord of hell's rules. What happens to the contractor in case the victim gets saved, though, is left a mystery, though it's possible that they go to hell instead of the victim.

Ai is pissed this season (Mitsuganae).
See above -- and then notice that Ai is no longer giving most of her victims that last chance. She's also been systematically destroying the life of Mikage, a totally innocent girl. In the past, innocent children have been Ai's only weak point, but it looks like her death in Futakomori has cured her of that; she's become more bitter than ever, almost sadistic. Her agents don't seem thrilled about it, either.
 * She lost her faith in humanity. Perhaps she have seen everything humans are capable to do, and just wants to send everyone to Hell. I wouldn't let the poor thing get all the guilt, though; Humans Are Bastards.

Ai's existence in Mitsuganae is maintained by those who seek her.
While it is true that Ai dies at the end of Futakomori, she seems to continue existing through Mitsuganae onward. This Ai may not be the same being as the Ai from the first two seasons. Even after she appeared to be gone, there were still those carrying a grudge they could not release. All this built-up hatred and bitterness maintains Ai's existence as a sort of thoughtform, In short, She exists because they want her to.
 * That would explain the change in Ai's behaviour, she is not really the soul Enma Ai but a kami or onryou created due to the belief people have in her existence. Thus she acts in a manner that they believe that the Jigoku Shoujo should act.