Filling of the loss cone by pitch angle diffusion will quench the growth of VLF waves that interact with substorm-injected electrons in the morningside auroral region. This occurs for any wave mode whose growth rate is sensitive to the anisotropy of the electron distribution near the loss cone. A pair of coupled nonlinear differential equations is developed to describe the coupling between the growth of waves and the pitch angle diffusion of electrons. The equations differ from those previously used to model repetitive precipitation pulsations (Davidson, 1979) in that the wave growth in the earlier model was assumed to be sensitive mainly to the total electron flux. The earlier model therefore was limited by the strong diffusion lifetime. The pulsation periods in the earlier model were too long and strongly damped. The new model predicts cyclic or repetitive precipitation pulsations for a wide range of conditions, with periods of 3--30 s, and negligible damping. The model agrees well with an extensive body of observational data.