Found same thing earlier today. 1. I'm sitting exactly above my router, since it's under the desk :D and 2. I already reset it twice today. Maybe the router is the problem, we bought it recently and I can't really remember if I've traded over WiFi since we got it. It's still weird, since we were able to battle and I can use the GTS, and Game Sync for Dream World just fine.
I really appreciate you Googling this for me as well, thank you.