I have this same problem, only mine goes dead in the Oct/Nov time frame.
Last time it happened was in November, on a road trip from Jacksonville, FL to north Georgia. After over three hours of driving we stopped for gas. The car sat 10 minutes at the most and was totally dead when trying to start. Luckily there was an Infiniti dealer in Atlanta that wasn't too far out of the way. After getting jumped, we headed straight there and the swapped out the battery.
Fast forward to beginning of this year while visiting dealers for my various cat/timing chain issues. The first dealer updated my software - the service adviser claimed there was an update to 'always' turn the alternator on. She claimed that on short trips, the alternator wouldn't always engage. That didn't sound exactly like the problem I was having, but hoped it was some kind of progress. Take that with a grain of salt, as the girl didn't seem super knowledgeable.
Dealer number two was of much greater help. He claimed there is a wire on the alternator that he cut for me that prevents the alternator from ramping down. Sorry for the vague info, it's been a few months since he told me about this. Apparently the alternator saves a few drips of gas a year by not running at full power all the time.
I'll find out if my problem is solved this fall.
Later,
pjdavep