Final Fantasy record keeper has something like this, dungeons you beat but didn't do well enough in you don't get "mastery" rewards.

Imagine if, instead of hard enrage you're all dead timers, if loot for raids was divided up into "hey at least you beat it" minor rewards and the good stuff, which required beating it in time.

And in Record Keeper, if you don't get the higher rewards you're welcome to repeat the dungeon.