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@booc1025, the FACT that your girl broke up with you first indicates that she doesn't consider your relationship more important than her family, she isn't willing to fight her parents about it thus what is there to fight for?
No matter how you feel, it is somewhat apparent from her actions that your girl doesn't seem to feel the same.
You could confirm with her if she still feels that your relationship together is still worth having. If it's only her parents are against it, then inquire what are the REASONS why her parents disapprove of your relationship? Do you know the answer to that?
Is it your age, both you and your girlfriend? Your financial status? Your personality or persona? Why do her parents dislike you? Why do you not have their approval?
If indeed in your girl's parent's view-- you are lacking and appear unworthy for their daughter, well the best way to save your relationship is to earn their approval.
Prove yourself to them as a person who has worth and character. Improve yourself in any way possible to meet their standards, if these are reasonable
If you do so, in the end you'll be a better person than who you are right now.