See if the problem persists. If it does, replace the modem. Installing
squid on your computer and configuring shorewall so that your computer
acts as a transparent proxy for all the computers on your LAN is a
good idea. You might want to go further and set up your computer to
provide email services to the computers on your LAN. Setups with
dyndns --- if you can't get a static IP --- work reasonably well to
receive your email directly. That frees you a great deal from the
usually ridiculous limits email service providers impose on their
users and greatly speeds up and easyfies things for the users on the
LAN.