Theory, observations, and simulations have shown that saturation of the cross-polar-cap potential occurs for high solar wind electric field. One of the parameters that affect the saturation process is the solar wind dynamic pressure. Theoretical arguments predict that higher pressure levels lead to higher transpolar potentials and a slower saturation process. The question arises of how the transpolar potential will respond to sudden enhancements of solar wind pressure in the saturation regime, and if the theoretical model predictions can replicate the observations. We use ionospheric flow data from Defense Meteorological Satellite Program (DMSP) spacecraft to calculate the transpolar potential and compare it with theory before and after a sudden increase in solar wind pressure. We find that the model predictions fall below the observed values for both pressure levels but are particularly lower after the dynamic pressure enhancement. The inclusion of a viscous potential, or the introduction of variable ionospheric conductivity, cannot remedy the discrepancy. We suggest that modification of the existing models to include magnetotail processes might be needed to bridge the gap between theory and observations.