it doesn't necessarily have to be a romance genre manga. as long as it has to do with the concept of going back to the past and "righting" the wrong or doing something they didn't get to do. also, no yaoi or yuri or shoujo ai or shonen ai thanks
They're both about past lives though, not going back in the past of the current one, but they're kind of entwined, especially Yukarism(plus it's a great manga imo).
Might also want to try Hajimari no Niina. Not exactly the same theme but similar kind of.
