I suspect that the problem lies in the shift mechanism within the axle. As HotRod said the dogs on the shift collar can get rounded off to the point that they will no longer stay engaged and the spring in the shift motor isn't strong enough to hold the collar in position. It could be locked in position with what you're calling a dummy motor; did that have a spring or did it rigidly lock the collar in position?
I once had a 57 GMC 450 with a 2-speed axle in the shop with symptoms the OP reported. Wouldn't stay in hi range. On tear-down, this turned out to be worn dogs on the shift collar and the gear it engaged. So rather than overhaul the axle, it was cheaper to buy one from a local breaker. But this turned out to be one from a 6-volt truck. I didn't know there were any 6-volt electric shift motors. I thought they were all vacuum in those days. I thought maybe is would just shift faster but no. I had to get a 12V motor. After which all was well. It seems unlikely that a new shift motor would be faulty but it does happen and it seems even more unlikely that you got a 6V motor by mistake.
