When we're young and in love, we do a lot of foolish things. I spent a year and a half in a similar on-again, off-again relationship. I was engaged to this girl three times in that span.
Take it from the guys who've been there, done that: leave this one behind NOW. Apparently this one will never be completely satisfied with you; the grass will ALWAYS be greener on the other side of the fence to her. Better to understand that NOW rather than after you get married; it's a LOT cheaper this way.
In my case, the girl in question finally married the last guy she left me for. But she was never really happy with him, and finally divorced him...and she's not happy now, either. As for me, I found someone who loved me, married her, had two kids with her, and stayed with her until she died way too young from heart problems, after 14-1/2 years of marriage. I remarried, and the current wife and I have 18 years on the books and counting.
And I've never looked back wondering "What if..." Because that's not productive...but looking forward with the one who loves me IS productive.