He can't take it from boredom within a month, which I think is fairly quickly even without comparing it to eternity.

If he plays a game of billiards, he magically sinks all 15 balls in the break. He wins every game he plays at the casino. His entourage of attractive women are functionally robots. None of the other people are real, because they definitionally can't be (and he's told as much). He's rich beyond his wildest dreams, but the money he spent his entire life scrounging for is suddenly meaningless. Even if he tries to make it so he doesn't always win (the example being wanting to rob a bank), he knows ahead of time a single numerical probability that he'll succeed.

And creature comforts only get you so far. Farther than a month until you can't take it? Probably. Although the burglar is portrayed as craving the risk-taking of his former life (edit: and reading between the lines, part of the reason it's so torturous for him specifically is because all he ever wants is to win). And it'd definitely happen eventually, which in the context of infinity is a blip.