Power Door Locks....hmmmm

If you have an alarm I think there might be two seperate relays. You need to locate all of the relays under the dash that are wired to the locks and check to make sure they are working (you know one does for sure). It is either that or the lock actuators are locking up and either need to be replaced or serviced.
I would check the relays first though.

One quick question, how hard is it to open the doors with the key?
If it is really hard, then that could be an indication that the actuators are going bad.

yeppers. do the switches in the doors unlock the doors? sorry if i missed that...

stangs use 5 wire reverse polarity locks. i dont believe there are any relays in the system (stock). your alarm could use external relays or have "on board" relays. for external relays, there should be one lock relay and one unlock relay. there will be more if you have priority unlock - not likely.

the lock and unlock harness should be at the top of the driver kick panel (or just below top of the inside of said panel). i think the primary colors for the wires is pink, but i could be wrong (and i dont recall secondary wire colors off the top of my bean).

normally the alarm relays are left in the neighborhood of the connectors and wires (like behind the kick panel there).

if you dont understand relays, it might be easiest to get a new relay (check the manual, but most alarms use bosch style SPDT relays) and put it in the socket and see what happens. you can also check for a pulse from the alarm upon disarming (normally a ground pulse to terminal 85).

good luck.

Hissin you are correct the lock wires are pink, I think with a black or brown stripe.