Just for what it's worth, I had a similar problem with my 2004 GMQ. The factory BCM died, and I replaced it with one from AZ that was guaranteed for life. Well, "life" was about 4 months. However, I kept the factory original controller, and opened it up and looked it over. There was a burned connection on the circuit board, so I soldered it back together, reinforcing it with some copper wire. I returned the aftermarket controller and got a refund, and put the repaired factory unit back in and it's been functioning perfectly for almost a year now.
Here's the faulty unit. You can see the burned connection.
Here's the repaired unit. Works perfectly now.
Regards,
Gene
2004 Grandma Marquis LS HPP ( With "MZT" and "SCT ": "The Undercover Marauder")
2004 Ford Ranger Duratec Flareside
1984 Ford Mustang LX Convertible