State-of-the-art low-power ECG hardware classifiers rely on extraction of pre-defined, hand-tuned features. This hinders their usage in different applications, because of the time-consuming redesign of features for any new classification task. As an alternative, we present a machine-learning based approach to ECG classification in hardware that still relies on feature extraction but is much more flexible to use. We utilize a recurrent neural network with temporal sparsity inspired by biologically motivated event-based systems. Features are extracted by freely configurable time-domain filters that are fully integrated in the training process. These are sparsified via delta encoding, so that further processing only acts on changes in the features or the recurrent connections. A scalable hardware architecture derived from this concept allows for stand-alone classification on input data streams. Despite its flexibility, our design achieves a peak energy efficiency of 37 nJ per heartbeat and an ultra-low power consumption of 532 nW in real-time operation, driven by temporal sparsity and a systematic low-power implementation strategy. At the same time, its classification performance is on par with state-of-the-art software-based classifiers.