Specifically the vehicles above equipped with the AM6C Automatic transmission

The AM6 box is generally considered a good transmission. But, they can have issues with the solenoids and valve bodies, usually when they get older (150,000 km +) which requires the valve body to be replaced (they wear out internally due to the housing being aluminium which causes fluid bypass). This often doesn't produce fault codes, and tends to be worse when hot They may produce a number of shifting issues but usually don't cause the ecu to veg out or drop into a limp-home mode.

If the Sport and or snow-mode lights are flashing this is generally not a good sign, and indicates a major problem. Ideally factory diagnostic software like DIAGBOX or LEXIA should be utilised to interrogate the ECU for fault codes. Generic test equipment is usually unable to delve deep enough into the system to be of any use. If the transmission is unhappy enough about the engine sensors to go limp mode then it will log 'remote' codes in the transmission ECU declaring its disapproval.