You pointed out earlier that this question would be incorrect due to the fact that the Na/K ATPase is still running during an action potential. Is there a membrane potential at which the Na/K ATPase either reverses direction? If so, would there be a brief period where it stops working?
My first thought when I read this was "I don't know," but let's consider the implications of a reversal. The Na+/K+ ATPase catalyzes the hydrolysis of ATP to ADP and inorganic phosphate. The exergonic nature of the hydrolysis reaction is coupled to the transport of the Na+ and K+ ions against both of their concentration gradients. Because there is a slight charge imbalance in the ion antiport (even though it doesn't "account" for the resting potential being negative), the transport also effectively works against the electric potential gradient as well. So, the normal function of the pump requires energy from ATP to act against the electrochemical gradient that exists across the cell membrane as a whole.
If the pump reversed, we would observe transport of the Na+ and K+ ions in the opposite directions, but we would also see
synthesis of ATP on the intracellular side of the membrane. Consider just how favorable the reversed antiport of the ions would have to be in order to
drive ATP synthesis via the pump. This would require an enormous electrochemical gradient (and if we want to only consider the transmembrane potential, as you specified in your question, we would need to determine how the membrane potential might become this great without changing the concentration gradients for the Na+ and K+ ions.) Further, reaching the point where the gradient exists with this magnitude would require passing through a time where, as the gradient increased in strength, the hydrolysis of ATP became insufficiently energetic to drive the pump's normal function.
I would speculate that if you could artificially establish such a gradient across the cell membrane, via increase in the strength of the existing gradient, you would pass through a point where the thermodynamic favorabilities of the two directions of pump function were equivalent, and the pump could stop (and technically, all this would necessarily mean is that the
net work by the set of pumps in the membrane is 0; you might have individual pumps going in different directions.) However, I wouldn't be surprised if establishing such a strong gradient caused the cell membrane to rupture altogether or something like that.
While yours is definitely a question for a molecular biologist and not something I'm qualified to answer outright, I would be surprised if the pump ever stops or reverses for the reasons you've suggested.