2001 Mercedes Benz ML430 Battery keeps draining

Electrical problem
2001 Mercedes Benz ML430 V8 All Wheel Drive Automatic

My car slowly dies (like a slow electrical leak). At first it will die if I don't drive it once a week, then once every 3 days, then once a day, but eventually it just dies. This happened last October so I replaced the battery -- obtained a brand new 6-year AC Delco battery. Went on vacation in January and when I came back the car was absolutely dead. It has, in the past, responded to a trickle-charger when this happened, and has been "jumpable" -- but not any more. I have also noticed that a small cylindrical object located immediately next to the battery will more often than not start whirring (motor sound) as soon as I connect the battery charger or jumper cables across the terminals, and I remember hearing this motor sound still running after the car was shut off back when it was still working. I've taken it to a shop which claimed that the battery held charge and that the engine didn't seem to be pulling more current than usual both on and off, but I then had to jump the damn thing to get it out of the parking lot! Any help would be absolutely appreciated!