You have three to four things that could be working to exacerbate this Dead Battery Problem:
(1) You have a
Parasitic Drain on the System that is strong enough to draw down the Stored Battery Energy in Less than an Hour:
You can diagnose this problem fairly easily using
THIS Tool and a Decent
DMM (
Digital Multi-Meter). Watch the Video for instructions on how to use BOTH of these Tools to get to the heart of the problem. If the OTC PD Tool confirms a Parasitic Current Draw is happening... then systematically
PULL ONE FUSE AT A TIME IN BOTH THE FRONT ...AND REAR FUSE BOXES until you can see a change and a drop in the the Parasitic Voltage Drain that you first recorded. This will pinpoint which System Component is either Shorting Out... or if it turns out to be a Module (BCM, LGM etc...) one that is
FAILING TO GO TO SLEEP with the Key OFF Position... then you will know where to look:
https://www.amazon.com/dp/B000RT81XW/?tag=gmtnation-20
(2) Your
Battery has NOT been charging long enough during so many Short Duration Trips to make a difference:
Even if your Alternator is Charging at around 13.5 to 14 VDC... if the time it takes to get to your daily destination is sufficiently brief... the Battery will NOT have enough time to Charge Back Up. In time... after so many Under Charges... the Battery Cells will suffer damage and begin to fail.
(3) Your
Alternator is Failing:
Test your Alternator. Start the Vehicle and Turn On Everything that will add to the Draw Down of Power and measure the VDC Output with a Voltmeter. If your Rectifiers are failing.... A working AC generator will not be able to convert that power to Direct Current... ergo... Dead Battery.
(4) Your
Starter Motor is Shorting Out or Failing:
After being Charged... If your Battery Voltage Tests prove nominal ... and remain at say 12.4 VDC AND if your Alternator is Charging with the proper Voltage after starting the Engine...neither Under nor Over Charging the Battery... Then isolate the Starter by using a Remote Starter Switch to Bypass the Solenoid Circuit using a Fully Charged Battery and/or one with an External Battery Pack attached. So if the Starter draws excessive energy and fails to Rapidly Turn Over... then you know the Internals of the Starter are BAD. Do this test... WITHOUT the Key in The Ignition. The idea is NOT to see if the Engine will start... You just want to see if the Starter Motor turns over 'Quick Like a Bunny' for at least 10-15 seconds and NO LONGER ...with obvious strength when doing so.
Be Patient,.. Be Logical.. and ...Be Systematic when using these methods and You Will Solve Your Problem(s).