My boys, can you help a brother out?

I've been with this girl for about 3 years. We have a lot in common and i feel like we could be perfect for each other, we are having issues tho. I'm thinking i should break up with her. When we have fights and arguments, she doesn't take blame or responsibility for her actions. In fact, she never apologizes, instead she blames me for her actions. example, we met her friends new boyfriend, and her friend asked us what we thought of him, i said he seemed like a nice guy and stuff, my girlfriend said, "yeah, you did better than me". i asked her what she meant by that and she said well, he has a better personality than you. of course, this pissed me off and we ended up fighting about it, and she was turning int around on me and saying jeez arent you going to let this go? and your always making a big issue out of nothing. She always makes comments that hurt me as a person, like she called me fat, said i sucked in bed, etc.. and when i got upset about it, she got mad at me for getting upset about it. She also breaks up with me a lot, id say over the course of our relationship she broke up with me 6 times, and every time we broke up she hooked up with her ex boyfriend. We have no communication is our relationship, everytime i want to discuss issues that were having, she doesn't want to talk about it, or when we do, everything is my fault. I kinda feel like im the only one trying in the relationship and i really love her but what should I do, she breaks up with me alot.