  Recent data indicates that the cosmic UV emissivity decreased with decreasing
redshift z near the end of reionization. Lacking evidence for very massive
early stars, this could signal a decline with time in the mass-averaged escape
fraction of ionizing radiation from galaxies <fesc> at z > 6. We calculate the
evolution of ionization fronts in dark matter halos which host gas in
hydrostatic equilibrium at its cooling temperature floor (T~10^4 K for atomic
hydrogen). We find a high escape fraction only for the lowest mass halos (with
M< 10^8.7 Msun at (1+z)=10) provided their star formation efficiency f_star >
10^-3. Since the low-mass galaxy population is depleted by radiative feedback,
we find that indeed <fesc> decreases with time during reionization.
