Whatever you do, don't fall for her stupid game. If you love her, why would you need to prove it? That's stupid. She should trust you. The real question is: Why is she with you if she doesn't trust you?

Sounds like a pretty futile situation, my friend, as you are totally at her mercy. Only she is the one who is in the position of saying whether anything you say or do is acceptable as "proof", regardless of how you feel or the amount of effort you put into it. The best thing to do is to accept it. Accept she feels as she does, and simply take the attitude "so be it". Why put yourself through untold suffering trying to find some secret that no one knows the answer to, perhaps not even your girlfriend. It sounds like she's not happy with you, and she's toying with you, to be honest. I'd let her know that if she's not happy with you, you can accept that, and perhaps it's best if you just broke up. First of all, it would get her to rethink the game, if that's what she's doing, and secondly, it would relieve you of forever being victimized by trying to find a way to keep her satisfied with finding ways to "prove" your feelings. Eventually it'll become too wearing to sustain, and the sooner you put an end to the game, the better. If she cares for you, she'll find a new appreciation for you. If she doesn't, why would you want to continue in a relationship where you're placed in such a pitiful situation constantly...?

there is no need for you to do something to prove that you love her she just have to believe dont stress yourself, if she love you she will see it maybe she just want to find an excuss to breakup with you, you dont have to do a thing to prove love

Well then you do whatever you can to prove it to her... Write her notes in the morning telling her how much you love her, each day make tell her something new you love about her. Do what you feel in your heart you can do to show her that you love her. It can be as simple as cleaning up after her after you eat or something as major as naming a star after her or taking her on a trip. Love can be shown an inturpretted in many different ways.

She doesn't want you and she is trying to get what she can for herself before she breaks up with you. She is not showing you unconditional love. She wants you to buy her something expensive. Love has nothing to do with it. Run the other way as fast as you can!