I'm having the same problem, but I have a lot more information about it.

I found that power cycling the modem restores the browser's ability to surf. Also, if I run the diagnostic tests that the network card controller has (which automatically cut off the internet connection until the tests finish), the browser can surf again.

I have a DSL modem/router/wireless transmitter, and a second, non-Dell computer also hooked up to it. The browser on the non-Dell always works, as does my PocketPC Dell running on Wifi. But the Dell desktop browsers will eventually stop working, Firefox will fail before IE.

I did a bunch of things that helped get to this point. One big thing was to uncheck the QoS Packet Scheduler under network connections properties of your LAN.

There's still a problem when the computer has been on for a while. I'm convinced there's some process that is unnecessary that is interfering. But my warranty expired a couple of weeks ago, and I can't chat with anyone anymore. If anyone has any further ideas, I would appreciate hearing about them.

I think I figured out how to maintain the connection. I downloaded connection keeper. I remember using this back when I was using aol with dialup. Aol would disconnect you after a period of time if it detected you were idle. I thought I would give it a try. So far it works just fine. Haven't been disconnected since I loaded it. It seems to work by making it seem like you are still surfing at all times, doesn't seem to use any resources nor slow down the cpu.
George