The issue is that the Begin() method for prop movers will only move the prop forwards once (as per my testing). You can use another method Advance() to move the prop in the “forwards” direction, which you define in the the editor by the arrow gizmo (I’m assuming you defined the down position to be “forward”).
If you wanted the prop mover to move up after calling Advance() (You moved the prop down), call the Reverse() method, which should bring the prop back to it’s original position. Do note that if you call reverse a second time, it will move your prop up again.
Edit: I think from my understanding, you are simply moving the prop mover to a new position, and then calling the Begin() method. The issue with this is that the prop mover cannot infinitely move a prop forwards from it’s relative starting position. It can only “move forwards” from it’s starting position at most once, so by simply resetting the prop mover’s position world position, the prop mover is still technically in it’s “forward location” relative to itself.