A theory of energetic charged particle absorption by insulating moons is presented that includes gyrophase dependence of the absorption probability when the gyroradius is not small compared to the satellite radius. This effect increases the average lifetime against absorption by factors of approximately 2 to 6 above previous estimates at Saturn. The sweeping lifetime then becomes significantly greater than the strong diffusion lifetime. A rigorous expression for the average lifetime against absorption, appropriate for a drift phase averaged radial diffusion equation, is derived assuming (1) a uniform distribution of gyrocenter equatorial plane crossing points in the sweeping corridor and (2) randomization of gyrophase. The pitch angle and energy dependences of the sweeping lifetime are found to be significantly different from the predictions of previous analytical estimates.