R6100 keeps dropping off-line for about a month after a power outage

I've had the R6100 about 1.5 years.  When we first connected the router, with phone support, it kept dropping off-line, sometimes over 10 times per day.  We returned the router twice thinking we had defective units.  Phone support said we needed a new NetGear modem, so we bought one.  Still the problem persisted.  After about 6 very frustrating months, the problem "magically" resolved itself.

Since then, every time we have a power outage, we lose connection over and over again.  Now, it takes about a month before the problem resolves itself.  Just trying to sign it here and write this message, I've lost connection 4 times now in about 30 minutes.  I've called my internet service provider (Cox) numerous times, and they don't show us dropping off-line.

Any advice would be appreciated.  Please know that I am very tech ignorant.