| You might check your alternator as well as your starter. Aspecific issue with the alternator could cause it to consume electricity even when the switch off. Also, a "dead" cell in either battery could cause both batteries to go dead.
If neither one of these is an issue, you might try removing both negative cables from the battery, and installing a test light between each post and each removed cable cable, so that all electricity consumed by the vehicle must pass through the lights.
Make sure everything is turned off, including the dome light. remove the fuse for the clock/radio and the ecm fuse. Begin pulling and replacing fuses (the same fuse that was taken out) until the light on the test light goes dim(er) or goes out. When this happens, it may lead you to the circuit that is causing the discharge.
I am not farmiliar with the static current draw of these trucks, if the static draw is too high, you might need to use an amp meter (multimeter) in place of the test light to notice the draw, but the procedure is the same.
Once you narrow the draw to a single circuit, you can dive into the specific issue to resolve the problem.
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2005 Chevrolet 3500 (Edge)
2005 Chevrolet 3500 Work Truck (5th Wheel)
w\ 45' Flatbed, 37' Van Trailer, 28' Van Trailer | 
O boy.....Probs Again!! 
Linear Mode
