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Bipolar = being severely depressed for a long time and then on a high for a long time. Unless he's been that please don't refer to him as Bipolar. It's a stigma that hurts many people as it's not what Bipolar Disorder is. Acting one way and then another isn't Bipolar Disorder. Not even in the slightest. It's suffering from severe depression for sometimes months. I don't think that's what you meant when you said that. You seem to mean he's "emotionally unstable" which could be a symptom of many things.
Anyway, he sounds like a jealous and immature guy to me. I'm not sure why you'd love someone who constantly breaks up with you. He's emotionally unstable and unfortunately there's not much you can do. If he isn't afraid of losing you then I'm not sure what there is to hold onto.