I have a radio controlled alarm clock sitting on the desk beside me at the moment which has exactly the same problem every so often. The second hand sticks in random positions. On my clock I find that giving it a good shake eventually frees it up and it will then run for a few months before sticking again. I’m just waiting to see if the shaking I have just given it is going to work and the answer is, not this time, it may be too worn now.
It had not occurred to me that the second hand was driven by a separate motor, obvious now that you point it out for the reason that you give.
The motor for second hand gets much more wear than the other motor and so will be the first to show any problems. My clock is more than thirty years old, just think how many times that second hand has stepped!
If I can’t get the second hand to step I shall do without it until the clock fails completely, it still keeps time, just no second hand.
Neil