I've been suffering through the same issue for several months. It comes and goes in waves where sometimes my router doesn't reset for days (at least I don't notice it) to having it reset hourly for days on end.
We are a huge user in my house with 2 desktops, 2 laptops, 3 DVR's and 3 STB's, 7 mobile phones, 2 tablets, 2 XBOX, 1 PS3, 1 Wifi printer, and maybe a few other devices. The router resets itself when sometimes I am home by myself with most of the devices off or even out of the house as often as it does when there are many devices in use at the same time.
Verizon has swapped my router 5 times nows, changed the ONT twice and had techs to my house on dozens of occasions. I figure that they have spent thousands of dollars in trying to fix things without ever spending a minute to research the problem. Each time a tech comes to my house they are clueless as to why they are there and what they are supposed to do.
I have had them question my power supply but I have tried numerous electrical outlets with and without power strips and nothing changes. I do not have power fluctuations and light that dim or get brighter.
I have had the techs tell me that the signal out of the ONT was low and was improved when the ONT was replaced. My upstairs has a second splitter and I know that the signal in some of the bedrooms is not optimal. If I unplug the STB in my daughter's bedroom it seems that this stops the resets from happening. I have told this to Verizon and they tell me that won't cause the problem and will not look at the COAX or the STB.
I am so fed up with these problems as I work from home 2-3 days per week.