I experienced the exact same thing as hogdoc.
It appears as if the router is doing a slow meltdown. Not everything stops working once you can no longer address the router directly but eventually it completely collapses.
I have the dlink network monitor widget up all the time and it loses the router before the, it seems, the degregation begins. It seems that applications already communicating with sites continue to work and the internet connection slows down.
I saw that applications such as pandora, netflix, news widgets, weather bugs and such continued to work as long as I didn't stop and restart the programs/device after web pages stopped loading.
When the router is working, it's great. However, this slow meltdown is unacceptable and must be fixed.