So when you say driven once a week, how far is the drive? In these temps and off only driven. short distance once a week would not give the car enough time to fully charge either.
If being driven for long enough then as above a temperamental alternator could be an issue (or a drain somewhere). I had the one on the X5 cause no ends of grief and every time the dealer tested it is was fine. I got them to agree to replace it and all sorted after that.
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