There are contradictory published data on the behavior of fluid slip at high shear rates. Using three methodologies (molecular dynamics simulations, an analytical theory of slip, and a Navier-Stokes-based calculation) covering a range of fluids (bead-spring liquids, polymer solutions, and ideal gas flows) we show that as shear rate increases, the amount of slip, as measured by the slip length, asymptotes to a constant value. The results clarify the molecular mechanics of how slip occurs. Furthermore, they indicate that in this limit, molecular dynamics simulations must accurately account for heat transfer to the solid.