Can this relationship be saved?

I have been with my boyfriend for 6 months now and we live together. I cheated once with him it was a quick one nighter and now he checks my phone, is always calling me, checking on me and accuses me of stupid stuff. I can't take it, but I love him very much, how can we get past this? he says, "old habits die hard." that is not fair especially when I am not now cheating and don't plan on it, I do care about him and am really sorry for what i did.....why can't he ever forgive me? what do i do?