Sounds a bit like my problem on a thermal control/data logging/data access via the web project but my web server stops after days rather than hours. At the moment I'm chasing the possibility of Brownouts being the cause. See http://arduino.cc/forum/index.php?topic=127394.new;topicseen#new
There used to be a problem with the ethernet library that could cause this sort of thing but that was supposedly fixed in the 1.0.1 release if the IDE
How big is your sketch? mine's massive at 29600 bytes and 360bytes of ram free (iand its still missing a bit of functionality). I consiously used only null terminated Cstring arrays and the (F("bla bla bla")) form for fixed strings.
I'd be interested in how you get on.