I had a similar issue with my 2013 6.0 gasser 3500. The battery would die after sitting for a couple of days. I finally discovered that, after placing jumper cables on the truck, the "ding, ding, ding" of the "key left in the ignition, door open" chime was activated. Only thing was there was no key in the ignition.
Turned out to be a bad cylinder lock in the ignition key.

Good luck with your issue.

Bill