I finally got around to correcting this problem. I had procrastinated because it didn't seem like much of a problem and was only a small annoyance when the radio would change from XM to FM by itself and the clock would not show the correct time overnight. That changed last week when it became a problem I couldn't ignore. Last Friday, my Wife and I drove to the gym without any problem. The AV started right up and ran OK until we got there. I shut it off, and immediately lost all electrical power. No dash lights, remotes wouldn't work, starter wouldn't engage, etc. It was just like the battery had disconnected itself just as I shut down. We went in and exercised for about an hour and I prepared myself for having to get a tow back to the house so I could troubleshoot the problem. I went out, opened the door, and the power was back on. We started the AV and drove home with no problems. I opened the hood to start the troubleshooting at the battery, and found that the side terminal bolt for the negative cable was loose - about half a turn out. I removed both terminals, cleaned them (even though they looked OK) and re tightened them. I did do a load test on the battery and it showed OK.
What puzzles me about this is how the loose ground connection was OK at the start of the trip, broke connection just when I shut the engine off, and then was restored by itself over the period of an hour. The loose connection was very obvious when I checked it when we got home but is a mystery to me that it would correct itself. We were lucky - didn't need a tow, didn't need to replace any parts, and the fix was easy and free. It was so basic that I kick myself for not checking it right away and a lesson that it is best to start with the very basics when troubleshooting an electrical problem.