Girlfriend still has feelings for her ex - what do I do?

Okay so my girlfriend and I have been going out for 4 months as of today and about a month ago she told me that she has been thinking of her ex a lot. So of course I broke it off and then a week we got back together we basically broke up on and off for like a month. The reason we kept coming back together was because she says she gets really sad even sick when she's not with me and she says she wants to forget about her ex. So I guess she says she has been trying to forget about him and I'm pretty sure this is the truth. So recently things have been going really good the past 3 weeks and then I brought up the question if she got over her ex and she said she almost was. She's trying and she thinks of him in a bad way and she doesn't see him or anything because she purposely avoids and ignores him. I just don't know what I should do should I give it a little longer because things are going good because we fixed some of our problems. Do I give her a chance to get over him? or should I just break up with her because I'm afraid that if her ex likes her again she might start thinking about him again but if she's over him then that won't happen so I don't know what do you guys think?
Girlfriend still has feelings for her ex - what do I do?
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