What can you never fold on the flop?
We are going to talk about 2 flops here.
Flop A: No pair on the board
I don't think I can ever fold top 2 pair in this situation, in fact I'll get all my chips in most probably if my opponent is making re raise the only exception being that all 3 cards are same suited and it appears that the opponent has flopped a smallish flush that he won't slow play. I might play the hand defensively then but still cant really fold it on the flop.
Folding top and bottom pair is also really difficult but I can fold bottom 2 pair on the flop.
Its also extremely difficult to fold AA on this board. If all 3 cards are same suited and I don't have the Ace of that suit and someone shoves then I am definitely folding. Otherwise its very difficult.
Flop B: Pair on the board
On this board I think I cannot fold trips with second best kicker or better hand. I can however fold trips with small kicker if my opponent shoves and he is a good player.
In fact I very much prefer to have top 2 pair on a board with no pair than to have trips with a weak kicker.