The radiation belt electrons in Earth's magnetosphere exhibit substantial variability driven by changing solar wind conditions. The electron dynamics are due to a number of different adiabatic and nonadiabatic processes that can result in rapid increases and decreases in the particle flux levels. In this paper we present observations of abrupt flux decreases driven by a moderate geomagnetic storm. The particle dynamics are found to have significant local time and energy dependence that developed over roughly a 10-hour period beginning with the onset of the storm. The electrons with energies greater than 2 MeV dropped fairly abruptly at various local times, but not simultaneously at different local times. It is shown that the initial flux dropout was due to the development of local taillike magnetic field stretching, rather than due to more global processes such as ring current buildup or large-scale radial diffusion. It is also found that while the lower energy electrons (E < 300 keV) fully recovered by the end of the storm, the >2 MeV electrons were lost from the magnetosphere and did not recover. These results indicate that the initial dropout of the radiation belt electrons at geostationary orbit was controlled by the adiabatic response to localized changes in the geomagnetic field that develop over many hours, but that eventually nonadiabatic processes acted to cause the loss of electrons from the magnetosphere. It is also shown that during geomagnetically quiet conditions, the energetic electron flux can remain at nearly constant levels for as long as 1 week, suggesting that in the absence of geomagnetic activity either the outer radiation belt electron loss rate becomes quite small or the loss and growth rates are balanced.