Boyfriend betrayal,,,what do I do?

My boyfriend and I have been dating for a little over 11 months. We moved in together 3 weeks ago. Back in November, I learned that he was "ting" his ex girlfriend. I confronted him, he promised to never speak to her, and we tried very hard to repair our relationship. There were a few times since then that I asked him if they had spoken to each other, and he told me no. Yesterday he left his email up on my computer and I found an email he sent to her in February with a link to a video in it. I immediately confronted him and he told me that she had contacted him wanting a they used to watch together and he forwarded it to her. He also admitted to talking to her on a few other occasions via text. I asked him how he could do this to me and he completely broke down. He cried and begged me not to move out and literally was convulsing. He seemed 100% sincere. I just don't know why he'd do this again if last time he knew that if he continued speaking with her it would be over. He told me he has no real reason he even responded to her, has no feelings for her, but yet feels bad to just ignore her (or anyone). They only dated for 4 months and she now lives across the country and has her own boyfriend. My boyfriend has an issue with keeping in contact with EVERYONE hes ever met. He tries to be friends with EVERYONE and talks to people when they make zero effort to contact him. He says this is because he used to not have friends when he was younger and you never know when you might need someone.Besides this issue, I love my boyfriend and we have an amazing relationship. Ive never had anyone treat me better. I want to know if there is a possibility for us to stay together and work this out. I feel so betrayed but know that he really treats me like a princess in every other regard. Is it worth me trying to work this out for him or is it probably going to happen again.