TWC has had some problems lately with connectivity problems and what not. Everything okay when you directly connect to the modem? If everything is okay then, then we know it's the router.
If it's NOT okay, then you need to let us know about your cable modem that is being used. Ambit, RCN, Terayon, Motorola Surfboard, etc.
Definitely tell us what your logs say. Internet cutting out can be literally ANYTHING.