DC motor starting and stopping
The average current of the motor may remain below 0.5 Amperes as noted, but transient currents could rise as high as 8.6 Amperes - the starting current of the motor would approximate the stall current rating. 

Secondly, a DC motor such as the one listed, would generate significant back-EMF (voltage spikes of reverse polarity) from the coil commutation.

Each of those factors may trigger protection circuitry of the power supply. From the description of the intermittent operation of the motor, it appears that the initial starting current drawn by the motor is causing the power supply to either enter short-circuit protection, or over-temperature protection. The supply then recycles, and restarts the motor, and the cycle repeats.

While current limiting may be an option, operation will still be marginal. Possible mitigation options:


Use a large value capacitor across the motor's terminals, to even out the current surge at start. This is unlikely to work with a 1 Ampere supply driving a 8.6 Ampere stall-current motor, the gap needs to be reduced further
Use a lower current motor, no higher than 1 Ampere stall current.


Even if you could make a motor work within the 1 Ampere limit with no load, any increase in load would inherently increase the current drawn, so measuring the average current with no load on the motor has no value for the intended operation.