I'm running RH FC2 2.6.5-1 on a Compaq laptop with an Athlon XP 2800+, 512Mb RAM, and a 40Gb HD.

Currently I'm connected to the internet using a straight ethernet connection to an RCA digital|BROADBAND Cable Modem and Comcast (Who have been absolutely horrible).

The problem that I'm having is that every 20-30 minutes, the transfer rates drop to 0K up/down, and the cable modem resets itself. After calling Comcast, they said that from what they could tell, the modem's fine, but to switch it out anyways. However, I noticed last night that when I was working with Apache, and tried to connect to the localhost while the cable modem was resetting that it wouldn't connect, which makes me wonder if it's something fixable on my end? I seem to recall that dhclient/dhcp leases and renews an IP, and had the problem of having to manually ifup my ethernet connection on another machine. Could this be related? I use the redhat-network-config dialog to activate my connection. Any help would be appreciated.

It sounds like a modem problem.
DHCP can be setup to give out leases for indefinite period .. It's unlikely that's a problem.
DHCP may rescind a lease, but can't do anyghing if someone is still using the address.
In the router DHCP is an added software module and it's has nothing to do with the router operation.