I can't believe so many people miss the question (or how the question was phrased).
First of all, Absolute nuts =/= Current nuts.
When do you fold the absolute nuts? The answer is never.
When do you fold the CURRENT nuts? In Hold'em, the situation is extremely rare, it would have to be a DON or Satellite where the
odds of getting potentially outdrawn outweight the odds of outlasting a super shorty.
Now in Omaha, there are tons of situations where folding the current nuts is the right play.
For example: You hold 23xx and the flop is A45 two tone. There is a pot-raise, reraise, etc. You may have the nuts right now but virtually any card on the turn assures that your hand is no longer good, and with no redraws.
Someone can have 3678 + the flush draw. Meaning any 2, 3, 6, 7, 8 or that suit is no good. Someone can already have a set. So now you don't want to see an A, 4, 5. That leaves us with the offsuit 9, T, J, Q, K.
In order for your hand to remain the nuts, you'd need two cards that are amongst: The offsuit 9, and an offsuit T,J,Q or K. if no 9, then any other broadway would put a higher possible straight. Sure, all outs are not covered. But we know for a fact that if the pot is multiway, someone is chasing the flush, someone has a set, and someone likely has a bigger straight draw. Someone could also be on the same wheel with a redraw.
23xx is not very playable in Omaha. But if you have say, AA45 on a 367 two-tone flop, with heavy multiway action, folding or as they say, "passing the nuts" may be the right play.