what model router? are you using Early Deployment IOS code and did you check cisco site for possible bugs
how much memory does it have? vs. amount of traffic being sent through
do a 'show interfaces' and look for tx and rx load
check your hub and cabling? sometimes cables and connections are ok until you start sending alot of data through it (go figure, tales from experience)
when this happens, is the route to the Internet still in the routing table?
'show ip route'
if so try pinging the next hop isp router from your router first. if you don't know their ip do a 'show arp' and look for the ip address with a '-' beside it (not your ip).
