Hello,
Resurrecting an old thread because I have the same issue. And for the same reasons! Went to a drive-in movie with my 2013 JX, and rather than the olde tyme speakers that hang on the car window, 21st century drive-ins broadcast the sound on FM. Using the car's radio, power shut off every 30 minutes.
I was turning on ACCessory mode correctly (one push of the ignition button without a foot on the break). Battery didn't drain, and didn't need a boost, but still annoying.
I searched the owner's manual and found mention of a warning "Power will turn off to save the battery," with the description "This warning appears in message area of the vehicle information display after a period of time if the shift selector has not moved from the P (Park) position."
But nothing on turning off the warning or extending the "period of time."
Any ideas?
Edit: In case Anthony comes back around, sounds like you hit the button twice, going past ACC into the ON position. That would explain the battery draining.