I've had the d790 for about 10 years now and have never had any problems. A few weeks ago I turned it on and instead of starting in Video 1 (that's where I've kept it) it started in tuner and went to station 87.5. All of my radio presets are gone and now everytime I start it up it goes to tuner and the 87.5. I've tried resetting the presets but they are all gone after I turn it off then back on again. I assumed that there was a small battery in there somewhere I could replace that kept track of that kind of thing, but the manual makes no mention of one. The only thing I could find in the manual was "The memorized station is maintained for approximatley one month even if the power cord is disconnected from the AC power outlet. If they are erased, store the stations again."
Dan; I think you are on track with the battery idea. Since it is 10 years old, and won't void the warranty, try opening the case and peering in. It would likely be a small quarter size button shaped battery on the main board.