We present experimental evidence and theoretical models that demonstrate that the slip length, which is the departure from the hydrodynamic no-slip boundary condition, cannot be constant as commonly assumed, but must decrease with increasing shear rate to avoid an unphysical divergence in the velocity of the fluid adjacent to the surface at small separations. The molecular origin of the shear rate dependence of the slip length is discussed. A new theoretical model for slip (the saturation model) is obtained, and it is shown to describe accurately colloid probe atomic force microscopy force measurements for all separations down to a few nanometers in two partially wetting situations (di-n-octyl phthalate on silanized silicon and bare silicon). Previous observations of slip length increasing with shear rate are explained as due to an imprecise calculation of the drag force on the cantilever. A new way of plotting experimental data is also presented, which provides a useful way to illustrate the slip length dependence on the shear rate.