If the above sequence is correct, then I would look for other problems besides the relay board.

1) Did anything happen to door electromagnet. Physical abuse, excessive water get into it, was it replaced, etc.
2) Did something happen to the door? Removed and replaced, door changer closed, ran into by a large cart, someone removed the mating magnetic plate, etc.
3) Does the electromagnet have the correct resistance, does it draw the correct amount of current, are the connections secure, etc.
4) Did someone touch the wiring between the electromagnet and the alarm panel? Did any other work get done recently that could have affected the wiring? Are the wires in the alarm cabinet in good shape, could a wire been broken, etc.
5) Is there fuse in the circuit that could have blown?

A simple continuity test and an amp draw measurement on a good electromagnet and then repeated on the suspect electromagnet, could answer a bunch of the questions.

LarryC