I think we need to go back to square one. If your using a static IP that was given to you from a block of IP for that building, and you keep having to reboot the router, theres a good chance your ISP doesn't keep ARP tables and someone else is using your IP. They can't use internet, they reboot, kicks you off. You reboot, kicks them off. And so on.
I would ask your ISP if they can check their routing logs and see if they see any other MAC besides your router using that static IP. Also ask if you can use DHCP as back up. If so, try changing to DHCP for a couple days and see if the problem goes away. If so, thats likly your problem, but without know how the network in the building works to bring you that ethernet connection in the wall I can't be sure.