I don't have bpd but I do exprience fear of rejection. From what you say, I think on a practical level you inderstand that not having sex doesn't mean she doesn't like you. She could be tired from a long day and the constant pressure can wreck your relationship.

Is there any way to change your thinking so you don't think having sex every day is proof of a successful relationship? Do you enjoy just hanging out together and relaxing at the end of the day? I never heard of mentalization, but it sounds interesting. I'm going to go read up on it now. Since you know she has low self esteem, maybe you can try to focus on making her feel better about herself and that will help keep you relationship stable and maybe reduce your anxiety.