This paper presents MobiQuery, a spatiotemporal query service that allows mobile users to periodically gather information from their surrounding areas through a wireless sensor network. A key advantage of MobiQuery lies in its capability to meet stringent spatiotemporal performance constraints crucial to many applications. These constraints include query latency, data freshness and fidelity, and changing query areas due to user mobility. A novel just-in-time prefetching algorithm enables MobiQuery to maintain robust spatiotemporal guarantees even when nodes operate under extremely low duty cycles. Furthermore, it significantly reduces the storage cost and network contention caused by continuous queries from mobile users. We validate our approach through both theoretical analysis and simulation results under a range of realistic settings.