It sounds as though the Final Exit contact has 'stuck'.
Give the part on the door frame a gentle tap with a screwdriver handle, don't over do it.
Try setting the alarm again, if sets correctly, you need to replace the contact.
If it still does not work, I still suggest replacement.
The screwdriver trick is just to give you a little confidence that you HAVE found the problem before any replacement.
Hope this helps.
Let us know.
acorn
acorn, May 2011