My dryer will not continue running after I release the Start button. Is there a latching relay inside? Does it have an electronic control instead? Could it be a bad moisture sensor? Sears Kenmore electric dryer. Model 110.63932101.

Several different components could be preventing your dryer from continuing to run when the start button is released. The wiring diagram and other technical information for your dryer are shown in the image below. When the start (PTS or Push To Start) button is pushed, the PTS contact is closed and voltage is supplied to the drive motor. Start voltage is also sensed through the blue/black wire that is connected to the P1-5 Start Sense pin on the control board. When the control board senses the start voltage, it normally applies 48 volts DC voltage through the Pink/Black wire to the motor relay to hold the contact closed between the two blue wires attached to the motor relay that supplies normal run voltage to the drive motor. With the start button taped down, the motor continues to run since it gets voltage through the closed start button. Since the motor stops running when the start button is released, it indicates that you have one of these 3 failures:
Broken or disconnected Start Sense wire.

Failed electronic control board that is not sending the 48 volts DC voltage through the motor relay Failed motor relay. Wiring failure between the components.
Since the motor relay and the heater relay are both exactly the same part, you could unplug the dryer and switch the motor and heater relay to see if the dryer will stay running. If it does, then you just need to order and replace the bad relay.

Maytag Dryer Won't Start - Testing the Start Button - YouTube

? 1:26
https://www.youtube.com/watch?v=gJwYV8HkTbk
Oct 7, 2013 - Uploaded by Bill Newberry
This video shows you how to test the start button on a MaytagDryer. ... dryer medc200xw0 will not keep running after releasing the start button.

GE Dryer won't stay on after turnin

Dryer won't continue running when start button released ...

forum.appliancepartspros.com > Appliance Repair Help > Dryer Repair

Jul 25, 2014 - 3 posts - ‎2 authors
When I push and hold the start button the dryer motor starts and heats. It will not continue to run when I release the button. All thermostats ... button released. Model Number: PYET344AYW Brand: Maytag Age: 5 - 10 years .... Check for 120vac on the purple wire at motor after releasing start button. If it goes ... GE Dryer will not stay running when start button released ...
2 posts
Jul 26, 2014
Starts but won't stay running
6 posts
Sep 12, 2013
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The digital control board has failed and is causing the dryer to turn off the relays that are supposed to Latch on

If the 'start' button used to latch in, the fix is to replace the switch. If it used to start by pushing in and releasing the start button, then a latching relay inside the case may be the problem. Open the top and check the relay that operates when pushing the button in. It could have a broken wire to a contact set or damage to the contacts themselves. A wiring diagram would be of help here. Good luck!

with power disconnected
follow the wires from the start button, to a relay,
check the wires (both ends) of all leads to the relay and reconnect any that have fallen off. (crimp tighter if they have fallen)
Check door switch function and connection.
check timer connections
the relay start-button timer and door switch comprise a latching circuit, when the start button is pressed the relay is supposed to latch closed and supply current to heater and motor. if the latching circuit disconnects the relay does not latch closed, and only runs as long as the start button is pressed.
if nothing has disconnected one side of the relay has usually failed, and the connection is not being made to latch the circuit
replace relay
relay is shown at right, 2 switches connected by a dashed line.

The start button is a low current signalling device that supplies power to a relay, the relay latches, to supply heavy current to the heater and motor, until the timer switch or door switch interrupt the latching circuit and disconnect the relay.
Relays fail
the connector for the latching circuit may have come off
examin inside the control panel for a device that looks like
, may be opaque or mounted vertically with wires connected to the bottom.
trace the wires from the start button, it should be the first device connected.
If any wires have come off relay, or other terminus of wire reattach and test operation of dryer
If no wires off, -replace relay
label carefully wires as they are removed, or replace one wire at a time, from old to new
generic dryer circuit looks like this
the relay is the two switches at right connected by a dashed line to show linked operation. Circuit diagram has no relevance to physical position of components

check also,

• the other ends of all cables connected to the relay,
  if the other end of any part of the latching circuit has loosened, the relay will not latch closed when the start button is pressed.
• Door Switch, it is part of the latching circuit

The start button starts the motor heater and energizes a relay that latches closed to keep the motor and heater running untill the timer switch or door switch cut the power to the relay and the relay opens.
The latching relay has failed or disconnected
if all the cables are attached to the relay
replace relay
not an expensive item, usualoly good for 10years
dryer circuits look like this, the start switch and relay are drawn just to the right of the motor, this diagram has no relevance to the physical position of the parts

the start button sends a electric current that starts the motor and latches a relay/solenoid. the relay is damaged and does not latch, it needs to be replaced, is not expensive, and simple to find with the model number given above, at your local parts store. buy the new one first, the store guy will tell you which panel to remove to locate the old one, I am unsure, just remove one wire at a time and place it in the same terminal on the new one.
the pic is a 'typical' wiring diagram (actually maytag) the start switch and relay are represented in the center.

Either the motor relay, or if this is an evenheat dryer, the evenheat control board could be bad.