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We present LiMoSense, a fault-tolerant live monitoring algorithm for dynamic sensor networks. This is the first asynchronous robust average aggregation algorithm that performs live monitoring, i.e., it constantly obtains a timely and accurate picture of dynamically changing data. LiMoSense uses gossip to dynamically track and aggregate a large collection of ever-changing sensor reads. It overcomes message loss, node failures and recoveries, and dynamic network topology changes. The algorithm uses a novel technique to bound variable size. We present the algorithm and formally prove its correctness. We use simulations to illustrate its ability to quickly react to changes of both the network topology and the sensor reads, and to provide accurate information.