The problem itself is with your cable signal. The HD signals show it most easily because they are using the most bandwidth and are most sensitive to signal strength problems. Digital SD channels are going to be a bit less sensitive, and the "analog" stations (the ones that are available with and without a cable box) will be the least sensitive. If your other TV's are set up without cable boxes or with non-HD boxes, it's to be expected that the HD setup shows the problem the most.

There's a setting on the Model 1070 called "auto polling" that can be enabled or disabled for each input. It will cause the receiver to switch over to analog audio when digital is not available. Try disabling it for your cable box input. That should significantly reduce the amount of time that the 1070 needs to recover from these cable signal drop-outs.