Dolly towing an Equinox

[Nuts]

Probably have as much trouble asking all you folks as I did talking to GM technicians about it but here we go?

During our last trip we had a problem with the Equinox towed on a dolly. Three times out of the twenty plus times I loaded it, when I went to unload the battery acted like it was dead! I say "acted" because it would start right up if I hooked up the 2amp battery chsrger and locked and unlocked with the fob? It would start right up and run normal not like it had a dead battery? This only happened three times, so the question is what did I do different those times that put the car into what appears to be a security mode ?

Your thoughts are appreciated.
Bill