We use measurements from the Lunar Exploration Neutron Detector (LEND) collimated sensors during more than one year of the mapping phase of NASA's Lunar Reconnaissance Orbiter (LRO) mission to make estimates of the epithermal neutron flux within known large Permanently Shadowed Regions (PSRs). These are compared with the local neutron background measured outside PSRs in sunlit regions. Individual and collective analyses of PSR properties have been performed. Only three large PSRs, Shoemaker and Cabeus in the south and Rozhdestvensky U in the north, have been found to manifest significant neutron suppression. All other PSRs have much smaller suppression, only a few percent, if at all. Some even display an excess of neutron emission in comparison to the sunlit vicinity around them. Testing PSRs collectively, we have not found any average suppression for them. Only the group of 18 large PSRs, with area >200 km2, show a marginal effect of small average suppression, ∼2%, with low statistical confidence. A ∼2% suppression corresponds to ∼125 ppm of hydrogen taking into account the global neutron suppression near the lunar poles and assuming a homogeneous H distribution in depth in the regolith. This means that all PSRs, except those in Shoemaker, Cabeus and Rozhdestvensky U craters, do not contain any significant amount of hydrogen in comparison with sunlit areas around them at the same latitude.