You will have to find a model number in order to get parts or help on this specific unit.
Find your model number - AppliancePartsPros.com

If you cannot find the nameplate see if you can get a part number off a part and then perhaps you can search using that and cross reference it back to a model. The timer is probably your best bet as it is used on fewer model than many other parts.

Your problem is weird in that you can restart the unit right away.
It will not be the moisture sensor as this just controls the timer motor.
On most units there is not a thermostat/heat sensor in the motor circuit.

The usual for a motor shutting off mid cycle is that the motor overheats and trips it's internal thermal protect but then you have to wait for the motor to cool down before it will restart.

Try it with an air only cycle.

My best guess would be a loose or bad connection in the motor circuit.
Also if the unit has a belt switch (down by the motor) check it. They will shut the motor off when the belt breaks but it may be that the switch or something related to it is opening.

M460-G Timer Switch? Any thoughts? Model #3977929 (I found it)
OK so I looked up 3977929 and it came up as a Control Panel but did show a number of units they were all REX5436 series.
I looked up the M460-G and it just came back as a microwave.
So I looked up REX5634KQ1 and when I looked at the timer picture it had M460-G on it.

Below is the parts for a REX5634KQ1 and the attachment is this units wiring diagram.
Parts for Roper REX5634KQ1 Dryer - AppliancePartsPros.com

From your description you have 4 possibilities:
1. The motor is over heating.
2: A loose/bad connection
3: The door switch
4: The timer contacts BU/BK

When it stops unplug it and measure across the BK/BU contacts. Should be 0 ohms. If it is the timer contacts they usually will shut the unit off at the same place in the cycle see if that is happening. Also try a different cycle type to see if it still stops.

If it is the door switch push on the door during a cycle to see if it will keep running
Sometimes the door latch weakens so that the switch is just being held closed then clothes hit the door and open the switch. Or the switch actuator bends so it does not hold the switch closed.
Could also be internal to the switch.