The problem is how you've wired the system up.
Devices nowadays will not operate if they do not see an incoming signal.
Somehow, you've wired your system so the DVR is not seeing an incoming signal when you shut off the TV (which is probably supplying the signal to the DVR).
Just sit down and draw-out the set-up you have, and think about what you need to rewire, to make it work.
If any other peripheral device is in your set-up, include it in your drawing (we can help if we see it, but we don't need to, you just need to think about what you have).
If any one instrument in the signal path is turned-off, or mis-wired, or a selector switch on any of those items is not in the correct position: the signal will not go to the DVR for processing.
Good luck.