What would you do to convince this guy?

My ex broke it off with me out of the blue a month ago. we were together 2 years had just bought a house together and had lost a baby last year. I really loved him and still do but he keeps saying im a cheat and a lier and thats why he ended it. I admit i cheated once in the first month of our relationship i told him and we tried again. SInce we bought our house though this has all resurfaced and he ended it. I was wrong to cheat but I told him as I wanted to start fresh or break away. I was faithful the rest of the relationship and always made time for him. I questioned him just before we signed for our house and he was still happy the a week after we signed he ended it. we still talk but he calls me cheat and lier yet wont tell his friends and family why we really broke up.im prepared to walk away from this relationship but i am still the mother of his first baby and it kills me he thinks so little of me. How can i convince him i didnt cheat all through our relationship