Difficulty repairing a lost connection

I have a XP Home system connection to a D-Link DI-624 router connected to a
cable modem. Intermittently, I lose connection to the internet. I've
contacted the cable company and they have assured me it is not on their end.
A strange thing that I've noticed is once I lose the connection to the
internet, I also cannot see or log into the router itself. Another thing I've
noticed is that when two people are logging into the system, I can't goto DOS
to attempt to repair the connection using ipconfig. Once I log one person
off, I can then goto DOS, do an ipconfig release all or ipconfig renew seems
to repair the connection.

My questions are why am I losing connection intermittently, why can I
sometimes repair the connection and sometimes have to reboot the system, and
why would having more than one person make the DOS repair options not
available?