But I don't see the modem and router models so I have to be vague here. Try the latest firmware in your router and put it on an UPS.
So basically I have internet through TWC (or Spectrum whatever you want to call it) and my router modem combo randomly resets. It does not turn off it just randomly has all of its lights flashing, the internet goes out, and I have to wait til it comes back. I contacted TWC they said it was all clear on their end, so I thought it was the router, so I got a new one, and the same thing happens. I have normal speeds and everything it just randomly stops. I am starting to think its related to my xbox because it does it the most when I am on it, but I am not sure, I have tried both wired and wireless connections and the same things happens. I have also changed channels, tried auto channel selection, and a bunch of other stuff but this doesnt make sense anymore. Help please.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic