Should I end the relationship?

I met my current boyfriend in a chatting website. We exchanged skype accounts and started webcamming and pleasuring ourselves every now and then. He later told me that the account was under a fake name and shared his real identity to me. We continued using the same account for about two months and then exchanged phone numbers and facebook accounts. About three months later we initiated a long distance relationship and decided to fly over and meet me in person. We met and had an awesome time and great sex. He went home and we continued having a long distance relationship. Every now and then I would notice that he was available/online in his fake skype account. I created a fake account and sent a request to become friends. I told him that I was from a different city and wanted to have a good time online and maybe meet one day. Of course, I never initiated the webcast but he was willing to have a good time online and maybe meet one day. Later I asked him why he still had that account and said that he will delete it. I trusted him and no longer asked him about that. Six months into the relationship, he stopped jerking off with me online. He never gave me an answer as to why, but he just did. We continued in a long distance relationship for two years. We would see each other in person every 2 months. We would jerk off one time every time we met, but never had sex again. Two years later, he moved in with me. We get along very well and really care for each other. The problem is that he avoids having sex with me. One day we were watching a movie in his computer when he received a call from his friend. He left the room to attend the call and while I was watching the movie alone, a message popped in the screen displaying a message in his old fake skype account. Long story short, he was jerking off and having conversation with different men online. In one recent skype conversation, he stated that he would travel to the city where his friend is and maybe meet. I confronted him and he said that the long distance relationship made him feel lonely. I found out that he never deleted the account and continued chatting with other men online, but not with me. He also said that he would never visit that person and that why don't I trust him. LOL. I told him that it was sad that he stopped having those online meetings with me one and half years ago, but he still remained in contact with other men. Anyway, he ended up apologizing and saying that he avoids having sex with me because he is not sexually attracted to me, but that he loves me and cares about me. Of course, that made me feel so insecure. We have been living together for about two months and he continues avoiding any sexual contact with me. Yesterday, I logged into his computer and found recent videos where he recorded himself jerking of with a random guys online. I keep telling him to open up and tell me how he really feels. That if he wants this relationship to work and that if he loves me. He says that he loves me and wants to be with me forever. He does continue saying that sometimes he doesn't really know what he wants. I keep telling myself to leave him, but I am giving him time to open up so that maybe we can work something out. Should I continue waiting or end the relationship?