Both steady and episodic sources have been proposed as sources of hydrogen observed by Lunar Prospector in association with the regions of permanent shadow at the poles of the Moon. Either source could supply significant quantities of water to the poles. However, space weathering processes affect the retention of water in the cold traps. We investigate those effects by simulating the evolution of a column of regolith in the region of permanent shadow over time. We determine the hydrogen concentration as a function of depth using a Monte Carlo model of discrete impacts and of delivery from the solar wind. We treat the delivery, sublimation, sputtering, and very small scale impacts as continual processes. Comparing the amount of water delivered to the poles to the amount remaining after space weathering, we find a retention efficiency of 5.6%. The retention efficiency of the polar cold traps is adequate for preserving volatile deposits over long periods of time. The average hydrogen concentration in the regolith column is 4100 ppm in the top meter after 1 Gyr. This is a saturation level in the regolith. Increasing the amount of time deepens the enriched layer but does not lead to increased concentrations. In 1 Gyr, about 1.6 m of the regolith is gardened. Therefore the top meter, which is probed by the neutron spectroscopy technique, has reached steady state in the simulations. The 4100 ppm saturation level is about half of the amount of hydrogen inferred from the Lunar Prospector neutron data.