The room-temperature longitudinal piezoresistance of n-type and p-type crystalline silicon along selected crystal axes is investigated under uniaxial compressive stresses up to 3 GPa. While the conductance (G) of n-type silicon eventually saturates at about 45% of its zero-stress value (G0) in accordance with the charge transfer model, in p-type material G=G0 increases above a predicted limit of about 4.5 without any significant saturation, even at 3 GPa. Calculation of G=G0 using ab initio density functional theory reveals that neither G nor the mobility, when properly averaged over the hole distribution, saturate at stresses lower than 3 GPa. The lack of saturation has important consequences for strained-silicon technologies.