Why do my boyfriend and I have such trouble communicating?

We've been together almost three years. We argue and he ends it by telling me he doesn't love me. It's hurtful because I am all about resolving the problem, and he dwells on the issue even if I drop what he's done and just swallow my pride and say I am sorry. How can this be resolved? We have kids, and I don't want a broken family because we can't communicate.