Most Helpful Girl
I believe there can be as many chances as there are as long as the party is willing to accept to give or receive another chance. As deragonus said about working through your issues helps a lot how a relationship becomes better, whether you fixed them while you were in the relationship or not. I had to grow up separately and understand how other people can be before knowing how much I love and adored my now fiance.
He taught me many things while we were together since I lived under a rock until I was 19, but I could not intake my romantic idealism be destroyed and he was there when I had mental breakdowns. It wasn't even destroyed per say, I was so exaggerated due to also my anxiety and depression and thought that changing any bit of my ideals to practical means meant he was not accepting who I was. In this sense your girlfriend's ideal might be questioned that she can never go back to an ex in fear that you may leave her again, that she would be a fool, or that it's simply illogical.
It will take some time, don't be just friendly with her but drop hints and affection to show that you care deeper than a friend for her to rekindle her emotions. Convince her with words to refute any doubts and fears that she has, let her feel like she has the reigns to call the relationship off this time if she needs to rather than make her feel she's forced into giving you another chance just because it's fair or smart to do. It'll also re-enforce for her to not leave you if she happens to get back with you because she might freak herself out that she dared go back to an ex due to passion and gets confused. Emotions are never logical, so she has to believe getting back together is safe, and more importantly, worth the risk again.