Folding AA in a donkament

Folding aces preflop is obviously never correct in a Hold 'Em cash game, but it is sometimes correct in tournaments when one sits on a cash bubble. Another situation might be when one possesses telepathic powers.

In the situation pictured above, the tournament is heads-up, winner take all. Hero has aces on the button, and Villain has shoved preflop blind, rendering Hero's telepathic powers useless. Throughout the tournament, Villain has held far more than his share of huge hands and has pulled off some astonishing suckouts, including one where he called a shove with 72o preflop and his opponent flopped a set, then died. AA is a 85-15 favorite against a random hand. What would the stack sizes have to be in order for Hero to consider folding preflop and waiting for a better spot?

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