Been there, done that, got the t-shirt
As others have said, there is clearly some reason you think you are not worthy of her and that she will find someone "better." First, you need to deconstruct this "unloveable" thing - recognize that it is not "True" with a capital "T" - it's most likely based on strange (il)logical leaps you made when you were a child in response to certain events.
Second, you need to recognize how frustrating it must be for her. One, you don't trust her, and two, you don't believe in her love for you. I was lucky enough to find a love who stuck with me through all that nonsense till I got over it, but many people don't have that kind of patience or insight. To them, it looks like you can't accept love when it's given, and like you don't trust them. If they leave, it just becomes more evidence that you're unloveable for you to use as ammunition against yourself in your next relationship.
Do yourself a favor and nip this in the bud. If you can, find a cognitive-behavioral therapist who can help you "unpack" your faulty reasoning. Meantime, recognize that just because you think something or feel something doesn't mean that it's true, or that you have to act on it.
Best of luck - if you can lick this, you've got it made!