So for Punisher.

Does the tokens only leave once the attacker or Punisher is KO'd?

It doesn't say they do... but in most cases, it wouldn't matter as they are removed from the game.
If you're talking about them being resurrected (eg. Lazarus Pit, White Lantern Ring, etc), it depends on how they are written as to whether they "would be KO'd" (meaning the tokens and everything stays as they aren't KO'd) or are KO'd... although as I type this, I don't think there's currently any game effect that could bring back a fully KO'd figure to the force it started on (and a couple that let them come back to your opponent's team or situations where the Punisher couldn't attack them anyway).

Did I answer your question or are you talking about a niche issue?

I guess let me reword it. After the attacker attacks after receiving the token does the tokens go away? or do they stay throughout the game?

If nothing tells you to remove the tokens then they stay indefinitely, or until that character is KO'd.

Ah, then yes, the powers that assign special tokens/markers that don't say when to remove it are removed from figures only when the figure is KO'd and only removed from the map at the end of the game... unless the rulebook has guidelines for removing it. Eg. an action token (ala Incap or similar) is removed when a figure clears, blocking terrain (not from Barrier, as that specifies when to remove them) can be destroyed with 3+ damage, etc... if a power has a special type of terrain on the map or a special token on a figure, they stay until the end of the game or the figure is KO'd.

Thanks burleigh and Dragon!