I am facing the same issue, only with a slight difference. My entire system sort of hits a halt, apps still work, but they refuse to close.
I am using Internet Sharing to share my internet connection from my iMac's Ethernet port to the WiFi. After a while, not only the iMac's internet stops working, the internet sharing stops working too, not to my surprise. Restarting the computer seems to solve the problem but not 100% of the time, and everytime I try to restart the system, all my open apps seem to refuse to close and I have to either force quit them, which works sometimes, or do a force shutdown by holding the power button for a few seconds.
Making the Ethernet port inactive and reactivating it does not solve the problem, nor does disconnecting the ethernet cable and reconnecting it.
I have a little software installed that monitors my network activity and displays it in the menu bar. I have it currently monitoring my Ethernet port and what happens when the internet connection stops working is that the Ethernet port, although still connected and with a green light, just stops sending and receiving data, sometimes it does receive some data but it stays at 30-60 B/s.
I'm sure this is an issue with OS X Lion because I had never had this issue with Snow Leopard until I upgraded to Lion.
Realy hoping for some guidance from Apple here on how to tackle this issue, it's quite annoying to have to restart my iMac all the time. I am used to leaving my iMac on all the time cause I access it remotely often using LogMeIn on my iPad. As well as that, I have other network services running and it's quite annoying to try and access my iMac remotely and find out it is offline because Lion refuses to keep me connected to the internet.