.dont remember which A1 or A1r.... whichever one or both has a battery in the ecu same as any home computer. There is several threads in here on trucks where they have had to replace the whole ecu cause battery in it was dead/going dead. Other users have pointed that this may be for the very reasons you indicate above as possible causation; while there is other threads that also point out that poor circuit board soldering of the Power Distribution Panel in a few years of the trucks may be part of it too.
One of mine with a 3126 in it sat for a month with no batteries.
When I finally installed them, truck fired right up and was good.
It is an A1 vehicle...