which may be the cause of this transistor problem?

1. Too much heat generated and the transistor internals suffered melt down.

You didn't mention the amount of heat-sinking you had applied to the transistor so this is a definite maybe.

2. Back emf from the DC motor exceeded the reverse bias for the base-emitter junction.

This is rated at -7 volts so be aware of this. Try putting a reverse diode across base and emitter. I would also put a 100 nF capacitor across the motor because if the potentiometer made a slight stutter and produced a wildly changing demand voltage at the emitter the back-emf generated from the motor's inductance will be high (potentially hundreds of volts).

Put a 100 nF capacitor across R2 as well (to keep the pot output steady).

which may be the cause of this transistor problem?

1. Too much heat generated and the transistor internals suffered melt down.

You didn't mention the amount of heat-sinking you had applied to the transistor so this is a definite maybe.

2. Back emf from the DC motor exceeded the reverse bias for the base-emitter junction.

This is rated at -7 volts so be aware of this. Try putting a reverse diode across base and emitter. I would also put a 100 nF capacitor across the motor because if the potentiometer made a slight stutter and produced a wildly changing demand voltage at the emitter the back-emf generated from the motor's inductance will be high (potentially hundreds of volts).

Put a 100 nF capacitor across R2 as well (to keep the pot output steady).

Also check that the BDX53C hasn't suffered - this could be another clue - maybe the BDX53 went pop (due to reverse base-emitter voltage (it is only rated at 5 volts) and, in turn, destroyed the BUV20 output transistor.