We propose a new formal framework for automatically recovering a class of reactive systems from run-time failures. This class of systems comprises those whose executions can be divided into rounds such that each round performs a new unit of work. We show how the system recovery and repair problem can be modeled as an instance of an online learning problem. On the theoretical side, we give a strategy that is near-optimal, and state and prove bounds on its performance. On the practical side, we demonstrate the effectiveness of our approach through the case study of a buggy network monitor. Our results indicate that online learning provides a useful basis for constructing autonomic reactive systems.