Battery drained repeatedly

Electrical problem 6 cyl Front Wheel Drive Automatic 500 miles

My aging mother purchased a 2009 Buick Allure (in Canada) new in the fall of 2008. Her previous car was a 1997 Cadillac Calais, which she has kept, thankfully, because this new Buick frequently will not start due to a completely dead battery. The Buick has been towed into the local GM dealership several times, where they have checked the alternator, starter, etc. And replaced the battery at lease a couple of times. They claim to have found nothing wrong with the car. The voltage gauge on the dash reads 13.8 volts while the car is running. The last time this happened (this morning), she had had it back from the shop for only 10 days, drove it 15 kms (10 miles) during the period, before it had a dead battery. It is in the shop right now as I write this. I have provided them with a C-tek float charger with a quick connect plug to mount on the batter so that my mother can have it charging between drives.

Their explanation is that she does not drive enough. You see, my mother only has 650 km (400 miles) on the odometer after a year. They explain that the many computers and electronics require the car to be driven regularly for at least 10 minutes a day.

I'd accept this answer if it weren't for two issues:
1. Her Cadillac always starts, even after sitting for six weeks. The Buick doesn't exactly seem to be bristling with technology compared to the Cadillac.
2. How will my mother ever go on vacation for 2 to 3 weeks anywhere, and return to a car in the parking lot that she can trust to start? This just doesn't seem like good engineering. It doesn't seem unreasonable to expect that a car should be able to sit for a month and start.

Could you advise:
a. Should we believe the service technicians?
b. Might the alternator be weak (perhaps not charging enough at 13.8 volts when the car is driven?
c. How much more electrical draw does the Buick have than the Cadillac (while the car is not running) and what is causing it? I'd like to at least understand what awesome electronics we are enjoying in exchange for the inconvenience of regularly putting the Buick on a charger. In this day of flash memory, how much power must the electronics draw to maintain memory and settings?

The GM technician told me that the draw was 8 milliamps when he tested it. I said "that seems awfully low, practically nothing". He responded by saying that this was what his test showed at the time of the test. Various computers and electronics go on and off from time to time after the car is shut off, eg. On star. He said that the car would have to be monitored constantly to see what is coming on and off, and then at the time of a large draw, figure out what is causing that draw. Help. This still leaves us with no answer and a car that may not start.

Thank you for your help.