We consider the problem of evaluating continuous selection queries over sensor-generated values in the presence of faults. Small sensors are fragile, have finite energy and memory, and communicate over a lossy medium; hence, tuples produced by them may not reach the querying node, resulting in an incomplete and ambiguous answer, as any of the non-reporting sensors may have produced a tuple which was lost. We develop a protocol, FAult Tolerant Evaluation of Continuous Selection Queries (FATE-CSQ), which guarantees a user-requested level of quality in an efficient manner. When many faults occur, this may not be achievable; in that case, we aim for the best possible answer, under the query's time constraints. FATE-CSQ is designed to be resilient to different kinds of failures. Our design decisions are based on an analytical model of different fault tolerance strategies based on feedback and retransmission. Additionally, we evaluate FATE-CSQ and competing protocols with realistic simulation parameters under a variety of conditions, demonstrating its good performance.