Why does my Linksys router stop working after 20-40 minutes?

I have a Linksys wireless router connecting my PC to my high speed cable. If I don’t use the router, and connect directly to cable, everything works fine. However, when I use the router, it works for about 20–40 minutes and then lose the connection. I have to unplug the power to the router, then plug back in. Once I plug back in, it resets itself and I’m back online until the next 20–40 minute span of time.

I tried the online help at Linksys, but that doesn’t address this issue.