I can't remember exactly... We had a number of discussions over about two years (I think), until in the end I met someone, and everything was more concrete and simple then.
It helped a lot that he fell in love with someone else too after a point, and switched from "I don't think that would ever work for me" to "wait, I'm poly too!"
It was hard at first though. He did take it personally. I think the fact that we stayed together showed him that it wasn't about him. Meeting someone helped him understand my feelings, too, so that was really good, even if it didn't turn out in the end.