I know EXACTLY how you feel. When I get into a argument (big or little) with my boyfriend he goes drop dead quiet. Its as if I'm talking to a wall. I get frustrated, as does he and then meaner thigns get said. Thngs only ever get solved between us when we see each other in person, the next time. During the argument, if I ask him what he's thinking, or how he sees the situation all he can answer is "I don't know" and he wants to drop the argument and have his time to himself. I hate fighting with my boyfriend, so I just want to talk it out, and solve the issue, when he just wants to leave me and himself alone to settle the frustration.(Better to talk when your calm and thought things through than in the heat of the moment...right?)
So I've learned to just shut up, and let him be, if he has something to say he'll say it when he's ready, and you two will eventually solve it. Give him his space for a while, but don't let the thoughts and argument build up(talk it out later) because it will make matters worse for the next time. It may be hard because you just want it to all go away, but sometimes only time will let a small or big matter heal itself. Guys are stubborn and just like us girls, we have our own way of dealing with different situations.