Originally Posted by hvac1000
It could be a relay or the motor could be going bad. Does the blower motor come back on after it turns off by itself? See if the motor is overheating. Let the blower run in A/C mode. Then when the blower cuts off TURN OFF THE POWER TO THE INSIDE UNIT and feel the blower motor with your hand. if it is real hot the motor is probably defective. I put the instructions in LARGE CAPS so you would read it and turn off the power for your safety.
If the motor is just warm then it could be the blower fan relay that kicks the motor on during cooling.