Has anyone's boyfriend skip a whole week not seeing you because of a silly argument?

Define silly argument for us first

Sounds shady as hell

That happens when there's no more interest.

"Skipped" a whole week, not "skip". Yes, lots of people's boyfriends and girlfriends have skipped an entire week. Millions of them every day in fact. Was that your entire question? Gee, great detail. He won't tell you where he's going. Again, WTF is your question? 

If he's blown you off for a whole week, it wasn't silly. But a silly way to lose him for good is for you to treat what clearly wasn't silly as silly and so, by extension, treat him and his unsilly feelings on the matter as silly. Maybe you should break up, though. You clearly don't care for him, much less love him. If you did, you wouldn't be so dismissive and invalidate his feelings as "silly."