Try powering off the deck before you shut off the car and power up after you start it for a few days. This will eliminate the deck booting up properly and or cranking power /running power.

 

Well, that was a good idea, but didn't seem to help much, or we didn't have the discipline required to do it for several days...
However, I just had the battery terminals thoroughly cleaned and the problem seems almost eliminated. It only happens now when I'm climbing a steep hill on the freeway, or taking advantage of the Odyssey's 300 HP V6 to blow away some unsuspecting muscle car from a stop light.
I think if I replace the battery entirely it will solve the problem. The alternator checked out okay.

 

I finally solved the problem with the audio dropping out during acceleration. Turns out it was bad E3 sparks plugs causing it. I guess they are way too hot for the stock Honda spark plug wires and were causing so much electrical interference that it knocked out the stereo when the engine was under load. I replaced them with NGK Platinum plugs and there is absolutely no static or interference at all with the stereo, even when I punch it. I had forgotten we put those plugs in the van, They caused a problem with my Accord as well and ended up damaging some components because their spark is way too hot. They also fail fairly quickly, probably by causing so much resistance that they overheat. They do not last 100,000 miles as the box claims. More like 10,000.

 

hahah one year later!!!!