I know it's not easy loving someone who keeps you at a distance. But you know, allot of great relationships started as friends first. The fact she doesn't want to cut everything off completely is encouraging. But allot also depends on what you want and how long you're willing to wait. Everyone makes mistakes in relationships. It's not all about forging, but about learning and growing. I'm not completely convinced that your prior errors are the problem but your girlfriends past trauma. She's been through allot and the walls are high and deep. She doesn't need convincing but time and patience for her to see things as they really are. Namely your stability and constancy.
She has a lot riding on her emotionally. She loves you and that scares her because she feels the wall getting a crack or two. That's a tough thing to handle when you've protected yourself emotionally and now find that protection weakening. Her heart is wanting to let you in but the mind is still in protective mode.
Time can help both of you in defuzzing your confusion. Taking things slow and really getting to know one and other will help strengthen your relationship and yourselves.