I have the same problems with TW. DNS just mysteriously fails, and the only fix is to reboot the modem. Rebooting the router doesn't help. And the really weird thing is that I've tried several different DNS servers, and experienced the same results with each. I tried TW's default DNS servers, Google DNS, and OpenDNS. Each of them would just fail at random, and I'd have no internet until resetting the modem. Which makes me think it's their crappy modems themselves. I've let it go, to test whether it will eventually fix itself. And it does, but it's anywhere from a few hours to days.
**** TW. Google Fiber cannot get here soon enough....
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