Accurate detection of pathological conditions in human subjects can be achieved through off-line analysis of recorded biological signals such as electrocardiograms (ECGs). However, human diagnosis is time-consuming and expensive, as it requires the time of medical professionals. This is especially inefficient when indicative patterns in the biological signals are infrequent. Moreover, patients with suspected pathologies are often monitored for extended periods, requiring the storage and examination of large amounts of non-pathological data, and entailing a difficult visual search task for diagnosing professionals. In this work we propose a compact and sub-mW low power neural processing system that can be used to perform on-line and real-time preliminary diagnosis of pathological conditions, to raise warnings for the existence of possible pathological conditions, or to trigger an off-line data recording system for further analysis by a medical professional. We apply the system to real-time classification of ECG data for distinguishing between healthy heartbeats and pathological rhythms. Multi-channel analog ECG traces are encoded as asynchronous streams of binary events and processed using a spiking recurrent neural network operated in a reservoir computing paradigm. An event-driven neuron output layer is then trained to recognize one of several pathologies. Finally, the filtered activity of this output layer is used to generate a binary trigger signal indicating the presence or absence of a pathological pattern. We validate the approach proposed using a Dynamic Neuromorphic Asynchronous Processor (DYNAP) chip, implemented using a standard 180 nm CMOS VLSI process, and present experimental results measured from the chip.