My boyfriend of 8 months has an ex girlfriend that keeps popping up in his life, what am I suppose to do?

They consider themselves friends but all they do is fight and bicker about stupid stuff (including my bra size.) They had a blow out about 6 months ago and stopped talking as he told her that she was "dead to him." Now over the holidays she felt the need to wish him a Merry Xmas since they spent almost a decade of holidays together and from there they believe it's a start to making things better between them. But this is the 4th (if not more) chance that he has given her to redeem herself. I'm at a point where I believe they should just let everything go and move on with their lives without each other, but my boyfriend wants to give her a chance. I feel like it's never ending. I have never been comfortable with their friendship because when they are on good terms it is just sentimental talk and it bothers me. They are both aware of how I feel but still it continues. What do I do? Is leaving the only option? I love this man dearly and I want to have a future with him, but feel that she is very unhealthy for our relationship. Should I just get over it then?