Assuming orig. factory alarm. There is a microswitch associated with ea. front door lock cylinder (and trunk). This arms/disarms the alarm. These are not available as a separate piece when I checked last and the whole deal has to be replaced if bad. They are suspect due to weather intrusion. There is a plug to the pigtails on this switch (gn.,yl.,br/bk wires last I saw one) that cracks at the wires insertion point and this can sometimes be repaired with a steady soldering hand.
The central locking system uses a separate swich on the actuator itself so this doesn't help the alarm any.
My bet is on a cracked green wire at the micoswitch plug.
The Golden Rule
1984 300SD (bought new, sold it in 1988, bought it back 13 yrs. later)