If there is "some fine print somewhere specifying a minimum usage" you should be able to find it in the owner's documentation that came with the car. I wouldn't count on the dealer to tell you about it. Hard to believe the car warranty would be void, but the battery warranty might be.
Have you found any such requirement?
This "auxiliary battery' must be a very small battery, probably to save weight. I can leave my non-hybrid car (with security system, radio presets, and all computers drawing the current they need for memory) sit for weeks at a time and the battery doesn't go dead. This happens on a regular basis, not just once in a while. It takes about 6-8 weeks before I have to worry about the battery, and if I know the car will sit that long I hook up my Battery Tender Jr.
It's also hard to believe these batteries are dying while the vehicle is being driven, unless the batteries are shot and the owners haven't replaced them.
I'd consider installing a standard car battery in place of whatever this "auxiliary battery" is and see if it makes a difference. "Delaying the inevitable" can mean many things. If you can delay the inevitable for a month or two you will no longer have this problem.
And, yes, the era of vaunted Toyota reliability ended a few years ago. They're still good, but not as good as they once were.
But, isn't that true of us all?