A few questions:
1) What type of internet service do you have? (Cable, DSL, FIOS, etc.) If you have anything other than cable, a common cause for your issue is that your DSL or FIOS modem already has a built-in router. Having more than 1 router in your system can cause IP conflicts. If this is the case in your situation, you will want to swap your router for an ethernet switch.
2) Do you have any other routers in your system? If you have a wireless router connected and you have not disable the DHCP (routing) function, this will cause IP conflicts like you are describing.
Let me know!
1) This is DSL service - I do not think its a combination modem / router. I do recall setting it to bridge mode so that the gateway does the login.
2)There is a wireless router connected but DHCP has been disabled.
I have been running with this setup for years and have had the problem intermittently though it has been happening much more recently. I did recently replace the modem. From your comment and and sequence of events I need to look at the modem setup to see if there is something there.
Nearly all DSL modems have a built-in routing function. It sounds as if yours does, since you mention having to put it in to bridge mode. Sometimes DSL modem/routers get out of bridge mode (maybe the provider does a system update or something else that resets it) and it goes back to routing. We have found that routers can "play nice" for long periods of time and then suddenly notice each other and have conflicts.
The ultimate solution for your scenario would be to put your modem/router back in to normal routing mode, and swap out your router for an Ethernet switch instead. A switch will expand your port count without any chance of IP conflicts.
Hope this helps!