Anytime I hear about a C1 misbehaving, I think about the power supply capacitor problems.

It's very possible that's a power supply starting to die - occasionally dropping voltage enough to lose the USB/Wifi, but not enough for a full reboot.

If that doesn't fix it, you can return it.

Did you try bringing it closer to the router to see if it helps? You can also try an Ethernet adapter to see if that works better and at least you can check to see if the wifi card is the problem.
I had a slight problem with my CC when I took it down stairs in a back room. The wifi card didn't seem to be as sensitive as the C1. If the power adapter didn't fix the problem it seems like the wifi card may be the next place to look. I think some have plugged in a wifi adapter in the USB to bypass the internal wifi card. Don't have details for that fix.
One last thought: I think the router cache on some router units get full and you may need to reboot the entire system and let it rerecognize the chumby. Some have limits to how many devices can log on in a given timeframe.

Thanks for the replies.  I have a spare Infocast 3.5 that I am going to try in the same location as the chumby one.  If the Infocast  works fine, then I will assume the chumby one has a hardware problem.

I think I have a spare wifi module for a Chumby One. If you determine it is a hardware issue, you are in the USA, are willing to pay cost of shipment, and I can actually find the darn thing, it MIGHT solve your problem. Let me know...

EDIT:
Looks like you are in the USA, so that makes it easier.