I am having the same problem. I had basic cable with a basic box and no issues. A few days ago Iupgraded to x1 with HD and after installing in the same place as the previous box it reboots about once in a few hour time period per day.
do you know the cabling in your home including where splitters are connected?
I have had this happen to me a few times only to the main DVR box. I have the X1 system and have a total of 6 cable boxes but it is always the main DVR box that keeps resetting. I have went to the local comcast store to exchange this box a few times. Each time the box last only two or three months then I have to go through it all again. Does anyone know why this happens? Do the boxes really go bad that often? Getting a little frustrated with the frequency of this happening. And yes I had to reset it 3 times during the super bowl!
Just a thought - my previous box (it had a digital clock on the front) used to run pretty warm. It used to reboot several times a day. I finally took it in and Comcast replaced it with a newer, much smaller model that has just a single light (no clock) and runs much, much cooler than the one it replaced. Never had a problem after that. It's possible that heat is your problem.