Airport Extreme Dropping Connection to One Device

Okay, here's my setup:

Cable comes into my Airport Extreme which provides a wireless network to the house (extended by a couple of Airport Expresses). There are some devices plugged in via Ethernet, too… my iMac and two Tivos. The TiVo in the living room regularly drops off the network. Sometimes resetting the TiVo helps. Sometimes resetting the Express helps. Sometimes plugging my MacBookPro into the TiVo's ethernet connection helps. But nothing consistent.

I've switched out the TiVos in the living room, so I know it's not the TiVo itself. I can plug my MacBookPro into the ethernet connection in the living room, so I know it's not the ethernet cable.

I've tried to tell the AirPort Utility to always accept the Network ID of the TiVo. That hasn't seemed to help either.