Originally Posted by Judder

Good idea - I tested both doors from outside and inside and the window drops correctly in all cases so I think we can rule out the handle as being the problem.

I also locked the car and tested the handles and they are correctly inoperative when locked so maybe it is one of the micro switches in the door lock not informing the alarm that the door is locked correctly?

Originally Posted by NuttyProfessor

I had this problem. It ended up being a faulty door lock unit. The door would shut and open just fine, but something electrical in the unit was telling the car the door was still open. Open circuit? Replaced that part and all is fine.