We consider a visibility-based pursuit-evasion problem in which a single robot with an omnidirectional but unreliable sensor moving through an environment must systematically search that environment to detect an unpredictably moving target. A common assumption in visibility-based pursuit-evasion is that the sensors used to detect the evader are perfectly reliable. That is, any evader that moves within view of the pursuer for any interval of time will be detected. This assumption is problematic because, when implemented on real sensor systems, such plans cannot account for the possibility of short-term false negative errors in evader detection. This paper addresses this limitation by introducing a model based on the idea of pessimal unoccluded distance to reason about the degree of plausibility that the evader may be concealed within each occluded region. We describe a decomposition of the environment that fully characterizes the opportune moment for an evader to take advantage of sensor error. Furthermore, we present a complete algorithm that solves the active problem of planning a search for a pursuer which maximizes the distance that the evader must travel through the pursuer robot's sensor footprint.