There are so many ways to tackle this issue I don't know where to begin.
You stated that you didn't have any additional electronics after market items on your Rig, which means that you have nothing else pulling any additional load.
So, that means we have to assume that the battery circuit can provide sufficient current for all components. That being the case, each component has diodes which limits and reduces the return voltage going back to the battery circuit. Given that, and given that this is a new issue from when you purchased the vehicle, one of your electrical parts is going bad, somewhere.
Like one of the other members mentioned, try removing individual fuses. Usually start with the radio, then work towards any dealer installed options.
Just as a sanity check though, you want to make sure that the alternator is working first, before the removing fuse excersise. Something is going bad in one of your components, and installing a battery with more juice is only buying you more time, not solving your issue.
Remember, all electrical circuits, including the battery circuit have a designed resistence and load capacity. Change any of those variables and you run into problems like theses as well as circuit cards going bad.
Additionally, if the dealer did a diagnostic on your Rig, and found no issue, then you are safe in assuming that the master circuit card is still working, as the diagnostic would have surely picked it up. So now the issue is elsewhere.
To really troubleshoot this correctly you need a schematic, which only the dealer can provide. But try removing individual fuses, that may guide you to your source problem.
Sorry this is so long winded.
Good Luck
