So your still losing internet connectivity? Does this happen on a regular basis/time interval? If so, see if connected directly to the modem (Other devices would not be online) if the internet connection stops working. Very possible the actual ISP/WAN connection is the culprit.
When this does happen, Can you still access everything on the local network? as in when your internet stops working, can you still share files between computers or send print jobs to the printer? This would indicate the router is working or if it is not working and help you determine if maybe a DSL/Cable modem will solve your problems