It's hard to tell from what information you posted, but it sounds like a hardware issue. Either something is happening with the driver or some piece of hardware is randomly shutting off (this happened to me before with an old ethernet card.)
I would suggest that the next time this happens,
1. Try pinging something no more than 1 hop away (the router, another computer on the network). Also try pinging YOUR IP address.
2. Type in /sbin/ifconfig
into the command line and check to see if your device is there (eth0?) with the UP flag on.
3. Copy the output of dmesg
to a file (dmesg > systemlog.txt
), reboot and post the contents of the file here.