Modems and routers should never be turned off. Only when stormy weather with lightning conditions are going on should they be turned OFF.
Ensure the phone line signal to the ISP modem is to spec for the modem and phone line cables are in good working condition. Swap out cables to test. Phone contact the ISP to help you with signal to the modem.
li] If this modem has a built in router, it's best to bridge the modem. Having 2 routers on the same line can cause connection problems: Link>
Double NAT and
How NAT Works. To tell if the modem is bridged or not, look at the routers web page, Status/Device Info/Wan Section, if there is a 192.168.0.# address in the WAN IP address field, then the modem is not bridged. If the modem can't be bridged then see if the modem has a DMZ option and input the IP address the router gets from the modem and put that into the modems DMZ.[/li]
[li]Check ISP MTU requirements, Cable is usually 1500, DSL is around 1492 down to 1472. Call the ISP and ask. Link>
Checking MTU Values[/li]
[li]For DSL/PPPoE connections on the router, ensure that "Always ON" option is enabled.[/li][/list]