Your boyfriend is obviously highly conflicted. You're in a very tough spot because there isn't much you can do to resolve his ambivalence.
Obviously, talking is the way to resolve his mixed feelings. But you really shouldn't be placed in the role of playing his therapist. Beside, you can't be unbiased. You are an interested party, so you won't be able to listen and understand him. When you talk to him, he will feel pressured by you.
The only thing you can do if force his hand. Tell him that you love him and want to be with him, but that you aren't willing to share him. You also aren't willing to be turned into a human yo-yo. Tell him that he needs to talk to a therapist to understand and resolve his conflict. When he has resolved his conflict and is able to say that he's not going to keep dropping you and running back to her, then you'll take him back.
Meanwhile, you can be friends. This is going to be a very hard stand for you to take, but it is the only way to bring this problem to a head and achieve a resolution. Not giving yourself to him, not being available whenever he wants you, and downright frustrating him, will force him to poop or get off the pot. Let me know what happens.