A robust real-world deployment of autonomous edge devices requires on-chip adaptation to user-, environment- and task-induced variability. Due to on-chip memory constraints, prior learning devices were limited to static stimuli with no temporal contents. We propose a 0.45-mm$^2$ spiking RNN processor enabling task-agnostic online learning over seconds, which we demonstrate for navigation, gesture recognition, and keyword spotting within a 0.8-% memory overhead and a <150-$μ$W training power budget.