Autonomic managers are the main architectural building blocks for constructing self-management capabilities of computing systems and applications. One of the major challenges in developing self-managing applications is robustness of management elements which form autonomic managers. We believe that transparent handling of the effects of resource churn (joins/leaves/failures) on management should be an essential feature of a platform for self-managing large-scale dynamic distributed applications, because it facilitates the development of robust autonomic managers and hence improves robustness of self-managing applications. This feature can be achieved by providing a robust management element abstraction that hides churn from the programmer. In this paper, we present a generic approach to achieve robust services that is based on finite state machine replication with dynamic reconfiguration of replica sets. We contribute a decentralized algorithm that maintains the set of nodes hosting service replicas in the presence of churn. We use this approach to implement robust management elements as robust services that can operate despite of churn. Our proposed decentralized algorithm uses peer-to-peer replica placement schemes to automate replicated state machine migration in order to tolerate churn. Our algorithm exploits lookup and failure detection facilities of a structured overlay network for managing the set of active replicas. Using the proposed approach, we can achieve a long running and highly available service, without human intervention, in the presence of resource churn. In order to validate and evaluate our approach, we have implemented a prototype that includes the proposed algorithm.