My gf has a painful background and has trust issues as well. If you've never dealt with someone coming from that place before, I can tell you that my impression is that this... worrying, not immediately being comforted by reassurances, etc... is very typical. It would likely be so whether you and she were poly or not. All you can do is ask yourself -- is she worth it? Is the relationship worth it? Yes, her issues do increase the possibility that it won't work out, but maybe it will. I would suggest that you don't break up with her in order to spare her feelings -- let her decide what's right for her and what's not -- but, rather, if you split up do it because this isn't right for *you*.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.