I bought a low mileage 2007 H3 in November of 2018. I spent most of 2019 working on it in one way or another. Passlock, not starting, shutting off, AC going to full heat when taken one click off max, wipers cutting on for no reason. I could keep going but you get the idea.

I bypassed the passlock feature. I checked all the grounds throughout the car. I replaced the battery terminals. I ran an independent power supply to the BCM. I replaced the ignition switch. And I kept having issues.

Long story short, the moisture that was shorting out the BCM and causing all of my issues was coming from the A/C evaporator. It was not draining out of the car through the drain tube (but it wasn't draining into the car either). One can of evaporator cleaner later and I have had no more issues. The evaporator drains onto the ground now and I have been driving the past 6 months without the first problem.

 

Pay closer attention to your Hummer. Mine always relieves itself. Cold days, out the tail pipe, rainy days out the sunroof drains, hot days out the hvac drain.

 

Like any machine These beasts were made to run.

Condensation causes all kinds of problems. Ignition and use is the cure...

Glad you solved your mystery issue.