The trouble seems to be pointing to the router.
What make, model and firmware is it running?
I had the same problem with an old Netgear DG834G v2, it would kick everyone off at 12 midnight, and a bizare work-around was to change the timezone for 12 midnight (as far as the router was concerned) was actually like 5am.
I'm not saying you have exactly the same problem, but it would help to understand if the error is at the same time EVERY day, or at set intervals, or is truely intermitten.
Also, if you have an Android phone, check out the Wifi Analyser app, it will show you what channels are being used. I'm sure there is PC software out there somewhere too.