I had a router that would require reboot to work also and the likely cause is the internal RAM/Flash memory is failing due to data retention issues. DHCP doesn't work but fixed IP would work. This is a fairly common problem brought on by high temperature inside the box.

For a long while I would spread the function into several different boxes:
Public IP address and DNS to DSL modem
Gigabit ethernet switching to external switch
WiFi to external WiFi router setup as an Access Point

This reduced the temperature inside the main router and it would stay up for longer time without needing to be restarted. It continued to be the Gateway, DHCP address holder and IP phone port. After a year or two, it finally gave up the ghost.