If the digital was unplugged, seems like we can rule that out as being a problem.
Go ahead and restore the system.
I realize I made a poor assumption. I would not have turned off the amplifier when messing with speaker cables. Most transistor amps don't care, and our amps don't care, so I always leave them on.
The fact that they are getting shut down is significant. As I mentioned earlier, the fact that messing with the cables gets a response is an important clue; turns out the amps were shut down during this time! They have become suspicious again.
The only bugaboo is that I think we did a test where the system was played until the bass dried up, then it was turned off for a while and restarted. The bass was still gone. But maybe it was not shut off long enough.
Next time the bass dries up, shut the entire stereo off for about an hour, then see how it sounds.