We analyze the feedback between neutral atmospheric winds and the electrodynamics of a stable, discrete auroral arc. We solve simultaneously, as a function of time, the ionospheric current continuity equation and the equation for neutral gas acceleration by ion drag. Our results show that, in general, the electric field in the ionosphere adjusts to neutral wind acceleration so as to keep auroral field-aligned currents and electron acceleration approximately independent of time. We thus conclude that the neutral winds that develop as a result of the electrodynamical forcing associated with an arc do not significantly affect the intensity of the arc.