HiCustomer Thank you for asking your question on Just Answer.
Do the accessories and radio stay on when you open one of the front doors?
It appears that you are having a problem with your "Retained Accessory Power" (RAP) function of the Body Control Module (BCM).
The BCM is located under the center console (between the front seats).
Below are a couple of PDF files that 1) tell how to test the system (which you have really done), and2) other steps to test if it will not operate.
RAP Other Steps
It could be just a "glitch" in the BCM, or it could be bad.
What I would do before I decided to replace it is to check that all the connectors are properly attached and there are no loose wires.
Take Care, Greg A.