Motorola Cable Modem keeps getting disconnected

I have recently started having a problem with my Motorola SB6141 Cable modem. Every day or so (Time of day isn't constant) I will lose my internet connectivity. I'll go up to the modem and see that it's flashing blue on the download icon. Power is on and upload is on. At first I would unplug the modem and the router, wait a few minutes (As per Time Warner's suggestion) and plug it back in. Usually it fixed it. But it's starting to happen more and more.

Recently, however, I realized that if I simply unplug the CAT 5 plug that goes to the router,  wait a few seconds, all of the lights on the modem will re-establish (including the internet globe light.) I can then plug the router back in and everything works for another day. So it appears that the router is somehow tripping up the modem?

Additional information:

Modem: Motorola SB6141
Router: ASUS TM-AC1900 Supplied by T-Mobile * (See additional notes below)
ISP: Time Warner Ultimate class


I want to stress I had this problem before I installed the T-Mobile supplied modem, although I feel like it has gotten worse. I also don't believe it's a cabling issue as I have recently moved and the problem has followed me.