Sorry about your door. Mine fell off too but fortunately I didn't loose it. But, to keep it from happening again, I put a small piece of black electrical tape on part of the door, across the hinge and onto the body. It's only about 1" long and 1/2" wide, and is perpendicular to and centered over the hinge so that it does not impede the operation of the door at all. The tape is very thin and flexes easily with the hinge. The tape on the body is mostly covered by an L bracket, so it's hardly noticable - if it matters.
This will not only keep me from loosing the door, but since the tape covers the hinge, I don't think it's going to come loose again in the first place. The door feels more secure when I open and close it with the tape in place than it does without it.
When you get your new door, assuming of course Nikon does eventually send it, you might try some electrical tape on it as a safety back-up. Works well for me.