Didn't see any definitive answers here or in my Bentley manual. So I called my local (West Palm Beach, FL.) Braman BMW dealer and told the parts rep my problem and asked her opinion for the part I would most probably need to fix it.

She advised to come in for a complimentary key "re-initialization". If the key doesn't work after that, or loses its ability to send the remote signals in the near future, then I need a new key. Thought I'd give it a try.

The service rep took my key, put it in the ignition, pressed a time or two on the key buttons, and then took it out. He then pressed the buttons to verify that the remote key worked. Indeed it does, from all angles, at 30 - 40 feet, first time, . . . no multiple presses. This is the original 2001 master key.

Unless it fails again, problem solved. I'd love to find out what procedure he used to "re-initialize" the key's remote capability to the car.

Love my BMW tractor - Darrell