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In long-term deployments of sensor networks, monitoring the quality of gathered data is a critical issue. Over the time of deployment, sensors are exposed to harsh conditions, causing some of them to fail or to deliver less accurate data. If such a degradation remains undetected, the usefulness of a sensor network can be greatly reduced. We present an approach that learns spatio-temporal correlations between different sensors, and makes use of the learned model to detect misbehaving sensors by using distributed computation and only local communication between nodes. We introduce SODESN, a distributed recurrent neural network architecture, and a learning method to train SODESN for fault detection in a distributed scenario. Our approach is evaluated using data from different types of sensors and is able to work well even with less-than-perfect link qualities and more than 50% of failed nodes.