Do you think people can ever find each other again in the future?

I was with my girlfriend for 2 years and 11 months, and I made some pretty terrible mistakes during that time period. I use to BMX so I was out 9-11 hours a day just riding all day and I'd completely ignore her. I also technically didn't cheat on her, I got this girls number and she broke up with me. And that happened twice. In June of this year she told me that she wasn't happy. When she told me that I instantly changed the ignoring her and everything else. Ever since she told me that I have been trying to be the best that I could be. July 9 we went to Kenny Wood and had a very good time, but we got into a few arguments, nothing major. She thought that my family blamed her for starting fights with me when I am the one who starts them and I admitted it to both of them. Next day I wake up call her and she broke up with me.. ): She said that she's not in love with me and stuff anymore. She says she hates me for everything I did...Well I changed and she's too blind to see that. Why can't people see when someone honestly, truly changes. I went from cheating on her,ignoring her, barely talking to her to NEVER ignoring her always making sure she's happy, etc. I know someone people are going to say "Once a cheater, always a cheater", Well that's not true. I think that if someone really does want to change, then they can. I feel like her and I belong together and she did at once point to. She wrote me a long letter explaining how she felt towards me and wanted to be together forever. She also included that "if we could get through all of this, then I know that we will be able to get though anything". Doesn't that include this??? I'm not saying that she has to be with me, I'm just asking if any of you think that there's hope that people run into each other again down the road and reunite.