Fallen question

PROBABLY A SPOILER - - -

So Fallen is about a girl who reincarnates every time she gets too intimate with a Guy who doesn't reincarnate but must suffer to see her die each time he earns her love. I don't really want a similar *novel*, but rather I think there is a greek myth very similar to this but i forget. I would appreciate it if anyone could tell me what i'm reminded of if possible.