My DH used to do this. Finally all blew up when he culminated in a 3-day sulk (not making eye contact, curt necessary communication only).
My crime? I had (very calmly and not snarkily!) pointed out on a car journey that this was why I preferred to leave 10 minutes earlier (entirely predictable heavy traffic that made us miss an appointment). We had had the discussion beforehand and he had dismissed the need.
I was so angry I just let rip that out of all the silly, minor things that happen in marriage, he deems this worthy of 3 days treating me like I don't exist. I told him I wasn't going to stick around just so someone could look right through me and that I'd rather give him what he obviously wants and leave him to himself (permanently).
He was shocked (I normally just ignore him until it blows over, but this was too long) and tried to blather something about needing space to process his own emotions.
We agreed that he can take time to himself being quiet if he wants, but that he must communicate openly that this is what is going on when I ask (instead of silence or denying a problem), and that deliberate avoiding of eye contact is disrespectful.
It works fine now. He can have his legitimate 'time outs', but he is not allowed to sulk me into an apology if he thinks one is due.