Should I give her a chance or dump her?

A week ago my girlfriend had stayed over at my house and her phone was lighting up with messages. When i went to put the phone on silent i noticed that the messages were to her best friend in which my girlfriend's ex was the subject of conversation. Apparently he was starting to see someone else and the message that threw me off was "I miss him like crazy". I confronted her and she explained that it was because of the idea that I wasn't happy with her the days leading up to that conversation with her friend. I was busy/frustrated with work at the time, nothing against her but she took it personal. She also mentioned she missed the mutual friends they shared while together. Now she's fighting for us to stay together and claims she has no feelings for her ex. Thoughts?
Should I give her a chance or dump her?
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