Poltergeists? .... My E39 unlocks itself at random. Any thoughts?

2002 E39. I have recently been leaving it in a rented space in a lot close to my home at night. Four times since I've begun using the lotI have returned to find either the driver's door or all doors unlocked.
First, even the second, time, I figured I didn't lock it. But the next two times, I know it was locked when I left it.
Anyone have any ideas what might cause this?
I've considered that someone parking nearby has the same key frequency? Not likely, but is it possible? Anyone understand the security to know if it's possible. If so, what's the fix? Parking where I live is near impossible at night and it took me a long time to get this space, so I cannot easily move to a new space somewhere.
Or, can there be something in the car itself that triggers the locks? Some weird short?
I have one key that no longer works on any of its remote functions and the other that has lost some of them (resetting the seat position for example) but still works the door locks. Could that be related?
Help please before someone else discovers that the car's unlocked regularly. Not that I leave anything of value in it, but....
much thanks for any advice.
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Personally I'd try to rule out some of the possibles.
If you can, take the battery out of the remote central locking keys, all of them, and go back to the "old fashioned" way of opening and closing the doors.
That way you can find if it's your own key fob is doing it.
Dodgy.
On Mon, 21 Jan 2008 14:14:32 -0800, reverse waffled on about something:

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MUSHROOMS ARE THE OPIATE OF THE MOOSES

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Except you can't take the battery out and the car won't start without it.

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The key fob only works for a few feet, mine says it works up to 200 feet, but as a practical matter I find it only works about 50 feet, and frequenlty less than that.
Operating the locking system the "old fashioned way" makes sense, sort of, but all one need to to isolate the fob is to take it out of radio range. Having said that, I can lock my car the old fashioned way and still unlock it with the button -- the point being that this is not a definitive test.

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