What should I do to regain her interest?

[Fusion_Tornado]

I've had this girl in my class like me for about 3 months now. The problem is that I have never talked to her, but she has attempted to flirt several times. I'm assuming that over time, she thought I didn't like her, so she just gave up a few days ago on flirting. Based on this, I think that she has lost her interest, or I might have broken her heart somehow. Can someone tell me what I should do to regain her interest? Should I flirt back? Also, if I want to approach her and talk to her, how should I approach her?