What about other electrical accessories? Stereo, Alarm, lojack, etc. something is drawing more current than it should. Maybe you have a stereo amp that is not turning off.
These suggestions aside, you need to start with the batteries, check the water level in them if they have removable caps, add distilled water if necessary. Next, get them load tested. New or not, it has been known to happen. If they check out, then disconnect the batteries and see if they are good after the 5 or 6 days that you are not running the truck.
If you still are having issues, then you will need to start disconnecting you electrical items one at a time to see what is causing the issue. Troubleshooting this stuff is tedious and time consuming. Good luck.