Knowing when to let go??

How do you know exactly when to let go of someone that you truly care deeply about? I'm asking because I have a little situation going on and I've known the person for a really really really long time. And we just had a bad fall out and it ended as if he thinks I gave up on him. But I wasn't giving up on him at all. I'm just really confused about it and now we don't talk. What on earth should I do???