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Im fairly sure that BMW key fobs (in recent times) 'shut down' after a period of some 15 minutes of being laid down and not moved, in an effort to stop 'keyless' theft by cloning signal.
A year from a battery seems not bad to me given how they are used, batteries do discharge by theselves when in circuit, used or not.
I do not know what the battery draw is on a modern key fob with BMW when in use, so difficult to say with any certainty.
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