Depends on the way someone is OP.
"Monstrously Overleveled/Overgeared/Overstatted" = Any situation wherein none of these actually help should be a failure.
"Astronomical amounts of pure bullshit/cheats" = Here's a rule you can't break, circumvent, or undermine. A limitation that cannot be overcome could cause a failure.
"Mental Health" = Doesn't matter if you can kill gods and lay universes low. In fact, I'd bet being able to do that would make depression a much, much deeper hole. Less morbidly, lines someone won't cross could cause failures.
"The Superman Problem" = Situations too complicated for any amount of power or competence to make a difference could cause a failure. Superman can't fix the American economy. He can't solve world hunger. What good is a god to those too far from the light?
"Amon Lee Hughman" = Basic human needs are inescapable unless you aren't human. What, fundamentally, is your character going to do on 0hrs sleep and no food in the last week? Not much, I'd bet. Doesn't matter if you can rip apart buildings with your mind, if someone shoots you with a 50. bmg while you're distracted, game over.
"Live Long Enough..." = Solving previous problems has turned the character into the problem. Something that no matter how many inches of OP-nis are applied, isn't going to change on its own.