Most Helpful Girl
I dated a guy like this once. Broke up with me for every little thing and it got to be exhausting. I saw the pattern though. He had no relationship skills. Telling me it was over was his way of me getting to react, cry, tell him I didn't want it to end. He was passive-aggressive and bi-polar so when he acted like this, it was his was of feeling some power.
Two things went on. It was either me doing something he was unhappy with and he'd pull this routine of telling me we should just split up, or else he would do something to which he could never handle being the ass and locked himself in another room and cut up his arms and legs. This manipulation technique would always have me reacting, feeling bad, and telling him what he did wasn't so terrible and ultimately I would apologize (yeah, me) for his screwing up for something.
This breaking up over and over nonsense is learned behaviour and she knows nothing else at this time to get your attention. I'll never forget when I told him "this is the last time you're going to say that to me because next time it really will be over". When he pulled his nonsense again, I stuck to my word. The look on his face was priceless, and I kept my promise to myself and really did end it. Best thing I ever did because soon after he became another girl's problem and did the same with her. I learned they had the same on-again-off-again relationship and she chose to marry him. She just signed up for a life of stress and pain. Better her than me!
Anyway, try that one on her. If she doesn't respect that you cannot keep going on this emotional rollercoaster then it's up to you to decide if you want to go the rest of your life living with a girl who will always put you through this. That very question was asked to me by my best friend back then. "Can you do this for the rest of your life?" My answer was no, and that's when I made the decision to say to him that that would be the last time he breaks up with me.