Is he acting this way around others as well, or is it just you? If the former...well, no matter how much you may want to support him, you can't force him to talk. Whether or not he chooses to confide in you in his choice, and whether you like it or not, if you're his friend, you'll respect his right to privacy and personal space and give him the time he needs to come to you...if that is indeed what he decides to do.
Sometimes, people face problems that they just don't feel confident or capable of discussing with others, and there isn't much you can do but give them time. You've made it clear to him that you're still there for him if he wants it. The ball, as they say, is in his court now.
If it's just you...well, if he won't give you an explanation, then you're better off without such a person in your life. If you did something wrong, and you're willing to apologise and make amends if necessary, that is all you can do. If he's not going to discuss disagreements maturely, it's a waste of your time to try and reach out to him.
Either way, you need input from him if you're going to continue being friends. It's frustrating and upsetting to lose people, especially if it's sudden and seemingly without explanation as this seems to be, but people are inherently self-centered creatures, and there isn't a whole lot you can do when someone decides to shut you out. I'm not saying you should forget about him and move on immediately - unless he's mistreating you - but right now, it sounds to me as though you've done everything you can.