Annihilation radiation from neutralino dark matter at the Galactic center (GC) would be greatly enhanced if the dark matter were strongly clustered around the supermassive black hole (SBH). The existence of a dark-matter ``spike'' is made plausible by the observed, steeply-rising stellar density near the GC SBH. Here the time-dependent equations describing gravitational interaction of the dark matter particles with the stars are solved. Scattering of dark matter particles by stars would substantially lower the dark matter density near the GC SBH over 1010 yr, due both to kinetic heating, and to capture of dark matter particles by the SBH. This evolution implies a decrease of several orders of magnitude in the observable flux of annihilation products compared with models that associate a steep dark matter spike with the SBH.