I would only fold AA if I was at a table of complete maniacs and have more than 4 people already all-in and I'm covered by most of them. Then the chances of winning the hand are extremely lower than usual.
Potentially also if it was at the bubble of a satellite and someone shoved before me and has me covered. Not worth the risk because the additional reward is not there.
Otherwise, I would never fold them. Why fold the best starting hand?
I even called an all-in of the big stack at the FT while I was second in chips and we were just two places away from the money.
He revealed QQ and unfortunately collected a set. It was painful but I'd do it again everytime.
If I'd won this hand, I was very close to win the tourney. This time it just did not work out.