Why does the alarm stay on when I shut off car, remove key and open door?

Not sure what you trying to say here. You drive the car, turn it off, park it, lock the door and the alarm goes off? Or all of that and the alarm goes off the next morning? If you are not turning off the alarm with the key in the door or a remote, the alarm will sound when opening the door. The alarm in this car arms itself each time the car is turned off.