AirPort Extreme drops connection with SB4121/TWC

We recently moved from an area with Cox Internet to a TWC area. We used our own SB4121 modem with a 5th generation Airport Extreme and it worked great with Cox. Now we're trying to setup internet with TWC, and I can't keep the router connected to the modem. It drops out almost every 15 minutes. What happens is, the wifi completely goes out and the green light on the front of the router blinks orange. The modem stays connected to TWC though. After a couple of minutes, it reconnects on its own. I've fully reset the router with no change. After many phone calls with TWC and visits with technicians, I connected the modem directly to my iMac and the modem and Ethernet cable work fine and don't lose connection. This leads me to believe it's a router issue. Any help would be appreciated!