A three-fluid model for the solar wind, with continuity, momentum, and energy equations for the three species protons, alpha particles, and electrons, including electron heat conduction and a parameterized coronal heat source, is used to study the behavior of the resulting proton and alpha fluxes as a function of coronal energy input and the proton-to-alpha density ratio at the coronal base. While in model solutions without alpha particles the proton flux is a strongly increasing function of coronal temperature, quite opposite to the observed near constancy of the proton flux in the solar wind, solutions with alpha particle abundances of the order of a few percent at the coronal base have a reduced proton flux and much less variation of the proton flux. The mechanism by which the proton flux is reduced is a pileup of the alpha particle abundance in the region of the coronal temperature maximum and the increased frictional drag on the protons resulting therefrom. We find a range of model solutions in which the resulting proton flux is almost independent of coronal energy input or coronal temperature, and we conclude that proton-alpha friction and dynamic accumulation of alphas in the corona can provide an explanation for the near constancy of the proton flux which is observed in the solar wind.