I had an e39 some years ago. The key was supposed to charge while in the ignition as well. It wouldnt hold a charge, and the dealer said new keys were not CPO, and would cost $400+. I stuck the key in my Sonicare toothbrush charger - And the keys held a charge - proving that the fault was in the ignition system recharge mechanism - which was covered under CPO. So maybe try a Sonicare and see if it works?
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