BEFSR41 Network Problem

I have lived with this problem since I installed the BEFSR41, and it
is driving me nuts so I need some help.

I have a Toshiba PCX1100 cable modem feeding a LinkSys BEFSR41 router
which feeds a LinkSys HPES03 Broadband Network Bridge for my HomeLink
network (phone line.)  I have two computers networked to the HPES03.
Everything works fine as long as everything is running.  However, when
I shut down one of the computers I cannot access the BEFSR41 with a
browser, and I can no longer access the Internet through the cable
modem.  The router just shuts the network down when I remove one
computer.  The odd thing is that I can add a third computer, and
remove it without any problem.  It seems that the router insists on at
least two computers on the network.  Any ideas?

Dick Hughes