Nightly updates generally occur in the 2:00 am - 3:00 am time frame to add new information to the program grid and shouldn't impact recorded program playback in process during that time. You could try contacting cox.help@cox.com to see if there is anything they can do, but you probably have a defective DVR that you will need to replace in order to fix the lockup issue.
If you email Cox, be sure to include your full name and the service address. You might also include a link to this Forum thread.
Update: If your DVR locks up immediately after using your remote while watching recorded programming, verify your cable TV is still working. Playback of recorded programming on a Contour 1 will continue after the cable TV goes out if playback has already begun. However, remote commands (fast forward, rewind, pause, etc.) require interactive access to receive a response back from a server and can cause the DVR to lock up until access is restored. (I experienced an intermittent outage once after starting a fast forward and it couldn't be stopped until it reached the end of the program). If you were somehow able to know a cable TV outage would occur at a specific time, you could start playback of a recorded program before then and watch it during the outage. Just put the remote aside and don't try to pause, rewind or fast forward.