I have A GE commercial coin op dryer that the coin op timer is not working. If I unplug it the time goes to 60 minutes. It counts down to 1 minute but never stops. This is the coin op timer assembly.

SOURCE: Electronic controls don't count down properly

Your problem is the electronic control board and unfortant that you cant repair or even get parts for it . Only if you get the whole control board will you fix your problem assy unless you find a good appliance man that repairs electronic control boards

SOURCE: Ge Commercial Coin-Op Dryer.

When you replaced the motor, did you replace the relay? It sounds like you have done everything reasonable. I would try bypassing the coin operation part and see if that changes anything. Go back to the motor relay. It may be incorrect application. the part guys only know what the computer tells them. it may need a different one. I am assuming that when the unit shuts off you checked for power from the timer to the next place, according to the diagram.

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SOURCE: Dryer runs for minutes then stops timer keeps going and going and .....

remove the vent on the dryer that goes to the outside start the dryer if it continues to ru n and not cut off you have a venting problem of the house

if it cuts off after 5 mins with the vent off you have a motor that is going bad

SOURCE: Timmer Maytag Commercial Dryer

the maytag timer for MDE10 should be a multi vertical slide in type. If so under the keyed panel on the top of the dryer, is an electric control with a grey knurled knob facing the front of the machine.
This grey knurled knob is the time set.
The knob rotates clockwise (from front) under motor control while the dryer is running, and jumps back to starting position under spring control when the slide is pushed in.
There is a single grey stud moulded into the front of the knob, that is the sixty minute mark, and a number of slots before the stud, that take a nylon peg. they are 6 minutes apart 54 48 42 36 30 minutes. Inserting a nylon peg in the slot at 30 minute will do what you want.
Most service guys drop the peg in the bottom of the control when they remove it, makes it easier to find, next time, so if there is not a peg in any slot, examine the floor if the enclosure, A short nut n bolt will accomplish the same result if the peg is not there.
If the original multicoin push in has been replaced with a newer single slot device I dont know how the change is made, none of my dryers are that new.

SOURCE: maytag coin op dryer timer programming for mde-16cs

The maximum run time on this machine's timer is 54 min. There is an adjustable peg on the white plastic index wheel which you can adjust anywhere from 30 to 54 min. For example peg in position E is 30min, D is 36min, C is 42min, B is 48min or for 54 min you have to remove the adjustable peg completely, but don't lose it in case you want to change the time in the future. If it is already in the Max "A" position and shuting off early you might have to change your torsion return spring. Hope this helps