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There is a bulletin(11-11-21) for the blower motor speed switch and the connector going bad. I have also seen the blower motor resistor go bad frequently. Since the blower motor speed switch is easier to get to I would start with checking it first. You can make sure the connector is not melted and check the switch with an ohm meter. The resistor is in the HVAC evaporator housing under the hood, it is behind the battery. To replace it the battery and the battery tray need to be removed.
The resistor has coils and it is possible the shifting of the vehicle is moving one and causing the blower motor to stop. The coils do corrode and fail.
lets start here