It's difficult. I'm pretty stubborn so I usually try to push past it. But if it goes on for too long, I get extremely bored really fast. Like, say that it goes on for a month or two. I might be all for pushing through it during that entire time, but then one day I wake up and realize that I'm just sick and tired of it. So I drop it.
If the girl you're chasing hasn't stopped sending you mixed signals over the course of a few months, you should probably drop it. Either she's just playing games with you (which can be fun for a short while, but tiring in the long run, and who's to say she'll stop once you get into a relationship?) or just really unsure of her own feelings (which isn't good either, because who wants to be with a person who can't decide if they truly like you or not...)
I wish you the best of luck anyway! I hope she comes around soon enough.