Should you be able to access your modem's web interface when the internet is down?

I have a Motorola MB7621 Cabel-Modem and D-Link AC1200 Router with Xfinity internet. I have been experiencing problems where my WiFi will be down for a few hours before coming back up. I have already tried restarting and factory resetting both the modem and router. Additionally, I know the problem is not a system wide outage because the XfinityWifi public network from other connections in my building works.

My main concern is whether the problem is being caused by a faulty internet connection to the coaxial outlet in my wall or the modem/router. Recently, I noticed that when the internet is down I can access the router web interface but not the modem web interface. During these times, the router "Online" light is blinking indicating that it is trying to go online and the "Upstream" light is blinking green indicating ranging in progress. Of course, when the internet is working I can access both. Should I be able to access the modem web interface if the problem is with the connection coming to my wall outlet? Or does this indicate that my modem is the problem and needs to be replaced?