UPDATE:
Last weekend, when we went for a drive, the immobiliser was slow to disarm. Not the usual two seconds, more like ten seconds.
When we came back after 46 miles with a hot cockpit, I re-tested it and it was back to two seconds.
So today I did a bit more experimenting................
It was cold in the garage, about 5 degrees C. I inserted the key and it was reluctant to disarm. So I wiped the side of the key against the lock barrel and it then disarmed. I put the key in the ignition but didn't start the engine.
With the key in place after 20 odd seconds the immobiliser re-activated. Note that it doesn't do this if the engine has been started.
I then connected the battery charger with the key still in place and within a couple of minutes, if that, the immobiliser de-activated.
Clearly then, this is a temperature/voltage issue. Cold temp reduces battery voltage........
After an hour on the charger, I'm back to a two second disarm when I put the key into the lock barrel.
Keith at BHM, and other dealers are aware of this issue.