We have observed depolarization effects when high intensity cold neutron beams are incident on alkali-metal-spin-exchange polarized He-3 cells used as neutron spin filters. This was first observed as a reduction of the maximum attainable He-3 polarization and was attributed to a decrease of alkali-metal polarization, which led us to directly measure alkali-metal polarization and spin relaxation over a range of neutron fluxes at LANSCE and ILL. The data reveal a new alkali-metal spin-relaxation mechanism that approximately scales as the square root of the neutron capture-flux density incident on the cell. This is consistent with an effect proportional to the recombination-limited ion concentration, but is much larger than expected from earlier work.