Aaron is this huge, hulking, preacher-gone-wrong version of Bane from The Dark Knight Rises, who just refuses to die. Let us repeat: He will not die. And not because he's immortal—he dies in the end—so there must be another reason that dude gets as many lives as a cat. Let's take a look.
Mayor Prentiss may be in charge of Prentisstown, but Aaron is the mouthpiece, the mover and shaker, the guy who loads Prentisstown up with lies and propaganda. And what better way to do so than to tell everyone that they're doing the Will of God? Aaron feeds the guilt of the people by constantly breathing down their back. His sermons are full of reminders that God is this awful, unrelenting guy who watches their every move (though this sounds a whole lot like Mayor Prentiss). Just look at this little interaction with Todd:
He leans down to me, his lips close to my face, and I can smell the breath that comes outta his mouth, smell the weight of it, like fingers grabbing for me. "God hears," he whispers. "God hears." (1.39)
See what we mean about Aaron being a preacher gone wrong? In this way, he's a bit of a shout-out to the biblical Aaron from the Book of Exodus, Moses's brother who epically screws up.
To be fair, Aaron's isn't the scheming, mastermind kind of evil—as Ben says, "Aaron is crazy. But the Mayor knows enough to use craziness to achieve his ends" (36.144). No, Aaron's more like the cartoon bad guy who holds a knife, grunts, and is always outwitted. Mostly. Because we can give Aaron credit for one thing: He knows how to manipulate Todd.
Aaron involves Todd in this cat and mouse game—and he always gives Todd enough fuel and clues to find him. For example, when he takes Viola and stabs Todd, he leaves him alive on purpose: "That's why he left me alive. So I could live knowing that he took Viola. That's how he wins, ain't it?" (26.54). Since Aaron's ultimate goal is to get Todd to kill him so the boy doesn't escape the Prentisstown cycle of manhood, we see him stoking the flames of rage within Todd throughout the book, trying to get him angry enough to follow through with murder.
Here's the thing about so many repeat encounters with Todd, though: As the story progresses, Aaron gets more and more mangled after each violent incident (thanks to things like crocodiles and Manchee's teeth). Todd tells us that Aaron's looks are something that will haunt him for a lifetime: "His face is a nightmare, a horrible thing I'm not gonna stop seeing even if I ever get outta this" (8.3). We kind of think Aaron would be pleased to hear this.
Aaron's mangled—but living—body kind of symbolizes how relentless evil is. It will die in the end, but boy will it put up a fight. "His face is torn and horrible […] and still, underneath all that, a look feroshus and devouring, a look without mercy, a look that won't stop, that won't never, never stop" (40.3). Luckily for Todd, Viola does put a stop to it. Phew.