Your'e losing digital data from Dish or the DVR. Since even live TV is through the DVR it is always a potential problem when anything glitches. That it doesn't repeat on immediate rewind/playback says the data made it to the hard drive ok.
The Denon is only defaulting back to an analog audio feed upon loss of the digital (preferred) one.
If it affects the video AND audio simultaneously the cause is something common to them.
I'd look at HDMI cabling into the Denon from the DVR.
Don't blame the Denon just yet.
I'd skip the video right past the Denon to the TV/Monitor even if it means using component cables instead of HDMI, but keep digital audio coming in from the DVR. Added cabling and connections never improve anything. Plus, HDMI cables are expensive.
It would be interesting to see if the problem comes back and affects only the audio or the video.
If you use optical cable make sure it has smooth flowing curves and no small-radius bends that would lose light power.