Offloading computationally expensive algorithms to the edge or even cloud offers an attractive option to tackle limitations regarding on-board computational and energy resources of robotic systems. In cloud-native applications deployed with the container management system Kubernetes (K8s), one key problem is ensuring resilience against various types of failures. However, complex robotic systems interacting with the physical world pose a very specific set of challenges and requirements that are not yet covered by failure mitigation approaches from the cloud-native domain. In this paper, we therefore propose a novel approach for robotic system monitoring and stateful, reactive failure mitigation for distributed robotic systems deployed using Kubernetes (K8s) and the Robot Operating System (ROS2). By employing the generic substrate of Behaviour Trees, our approach can be applied to any robotic workload and supports arbitrarily complex monitoring and failure mitigation strategies. We demonstrate the effectiveness and application-agnosticism of our approach on two example applications, namely Autonomous Mobile Robot (AMR) navigation and robotic manipulation in a simulated environment.