Linksys router loses connection after a while

Network was:

AT&T Broadband ISP
LanCity LC-PET3 cable modem (non DOCSIS)
Linsys 4 port hub
2 Win98SE PCs
All worked fine

New network is:

Same as above, with a Linksys 1 port router (BFSR11) between the cable modem and the hub.

Router is configured to be a DHCP server (default configuration).
I assigned the router a custom WAN side MAC to match one of my two PCs to avoid having to call AT&T to get things running.

Results:
Everything runs perfectly fine initially, but after leaving and coming back to either system (left on, in standby) after quite a while (going to work / bed), the network connection is dead.

WINIPCFG still reports the same IP, but seems to hang forever if I attempt to release / renew.

The router's is unreachable for configuration / status (it's still on the default IP of 192.168.1.1)

Pressing the reset button on the back of the router restores the internet connection (quickly too - I'm back online in about 15 seconds).

Entering standby manually and coming back out again after just a couple minutes does not affect the internet connection - it seems to only occur when I'm off for an extended period of time. I have no had the time to determine what the period of time is, and if it is a fixed time since DHCP lease / initial startup, or if it is a fixed amount of inactivity time (or maybe even not a fixed amount of time at all).

I'm hoping someone here has some ideas for me?

Thanks!

Not sure what setting you're referring to? DHCP lease lifetime is set to "0", but according to the on screen info that means one day.

I have no DNS addresses entered manually in the TCP IP settings. When the internet connection is working both systems are receiving DNS addies (winipcfg shows them). But when the internet isn't working it's totally dead - can't even connect to the router using an IP address, so it shouldn't be a name lookup issue.

When I first got it (purchased new just over a week ago) I flashed it to the latest firmware. When I started having trouble I tried flashing it with the previous version. Both versions show the same problem.

That's quite possible (that I have a dud). Just for a sanity check I switched back to "cable modem <-> Hub <-> 2PCs" last night and it had no trouble at all (was still connected in the morning). With the router in there things run fine, but are always dead after a few hours. I have never had it die on me during use though.

Some kind of time out? Maybe I should try using one of those "keep your connection alive" utilities that people use for dial up or DSL connections that have timeouts?

I'll try to find one at a local store that I can pick up to test if mine is screwy. If the new one is fine I'll get the intermittent one replaced.

Thanks!