There is one situation where you should 100% fold AA: near the bubble of a satellite. If you know you have enough chips to hold your ground until the bubble burst, there is no need to risk your stack, since all places paid get the same prize, a ticket to another tournament. If you just fold every hand for a while, you'll get your ticket, while if you play your AA you might end up getting a bad beat and missing the opportunity of playing the tournament to which the ticket was valid.
In any 1v1 situation, folding AA preflop is not profitable in the long run. Of course, if there are only two players with huge stacks and you're one of them and the other puts you all in preflop, you might decide to fold because of ICM and I won't blame you. A bad beat there could make you lose a guaranteed cash. But if you're risk neutral and want to win the tournament, that is a spot you would love to be.
Against multiple all ins, AA lose a lot of
equity. You're probably still getting good enough
odds to call, but survival is an important thing in a tournament and you will probably end up eliminated in a hand like that. If you win, you'll have a huge stack, but more often than not you'll be out. If you believe your poker skills are better than most players' there, you might be better off folding and growing your stack slowly but consistently.