Blower motor stops running after few minutes on 2007 Dodge RAM 2500 ?

This problem is not very common.Its quite possible that blower motor resistor is faulty and needs to be replaced.
But if you have already replaced the blower motor resistor ,then the problem could be faulty/weak blower motor itself or the issue with control head,its getting short and this problem is caused.
Do this the next time the motor stops: take a jumper wire and connect one end of it to the dark blue wire at the blower motor. Then ground the other end of the jumper wire. If the blower motor comes back on, then suspect a problem with the control head. If the blower motor does not come on, then replace the motor. While you are checking this, take a 12 volt test light and verify that there is voltage on the pink/light green wire at the blower connector.There are two wires going to motor, a solid blue on and a blue/yellow.Ground that blue/yellow wire. If the motor is ok, then it should come on full speed. If it does not come on full speed or not at all, then replace the motor.If the motor checks out ok,then problem is with control head.It has to be replaced.

This details will help,Thanks.