Sorry for the very late update. I did end up figuring out the use. The battery was bad. I tested it by removing the battery and running on just ac power, and it ran fine for hours. I ended up replacing the battery and it worked fine since.
Not 100% sure, but I have a few things you could check. 1. Have you checked your voltage on your battery connections while running and not running to ensure your alternator is charging? 2. Do you have anything plugged into the cigarette lighters/ power jacks on the inside of the truck over night? Aftermarket stereo installed? Radio unit, amplifier, or subwoofers? 3. Alternator: Brand new or refurbished? Sometimes refurbished units can be bad.