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That's what the pump is there for. In practice, very few ions move during an action potential. For this reason, there is a quite small effect of action potentials on the concentration gradients that in turn (with selective permeability) constitute the battery. With no new energy supply (a "dead" worm or whatever) you can get lots of action potentials before the concentration gradients are reduced. But yes, over time the concentrations gradients will "run down". Life includes continually re-establishing the concentration gradients/recharging the batteries.