Complex systems can exhibit autopoiesis–a remarkable capability to reproduce or restore themselves to maintain existence and functionality. We explore the resilience of autopoietic patterns–their ability to recover from shocks or perturbations–in a simplified form in Conway's Game of Life. We subject a large number of autopoietic patterns in the Game of Life to various perturbations, and record their responses using multiple resilience metrics. Our results show that while resilience is rare, we are able to identify structural features improving patterns' resilience. We also draw several parallels between the resilience of patterns in the Game of Life to real-world complex systems. Our work may be useful both for improved searching for resilient patterns in the Game of Life, and for exploring resilience in complex systems.