Relationships end. Its not something to be ashamed of. They have to end so that incompatible people can move on to find someone more suitable. Notice I didn't use the word 'better'. Its not a judgement about your value (or it shouldn't be), its about mutual compatibility, or not.
That said, if she broke off b/c of issues that you can address, and you work on them in good faith, you might be able to tell her this. You could ask her this. Oh, and hoping she'll come back isn't likely to work if she has actually left the relationship. Women tend to wait until (or past) the bitter end before they fly. Ask any naughty husband who tried to reconcile with his estranged wife--unless he really makes good, she's gone. Good luck.
Second thoughts can generally be amended with judicious action; injudicious actions can seldom be recovered with second thoughts.
--Cyteen by C.J.Cherryh