The funny thing is, if you DID decide to give up hunting for her, she would surely lose respect for you anyway. You said you like her and wanted a relationship with her and she gave you the LJBF ("Let's just be friends"). Perhaps she gets a kick out of seeing what she can get you to do for her and controlling you.
Or maybe not. Either way, just do what you want and disregard her games.
Or maybe not. Either way, just do what you want and disregard her games.