Looks like my timeouts were caused by how I had my router configured. I set the "max connections" and "inactivity timeout" settings to the recommended values for P2P use. That is to say a higher number of allowed connections (4096 instead of 512) and a shorter timeout (120s vs. 3600s).

That may not be your problem, since apparently you see the connection problems and roomie doesn't. Though, if he's playing mortals, maybe he just never reaches the required level of inactivity for the connection to be severed?