Active replication on top of a structured peer-to-peer overlay is an attractive solution for transparently providing high availability to distributed applications. However, self-healing is necessary to ensure the availability of the replicated application despite node arrivals, failures or departures in the overlay. Self-healing means to automatically reconfigure the replica groups when changes in the overlay occur. In the case of active replication, reconfigurations must be done carefully, to keep the replicas consistency. Moreover, as every reconfiguration could imply a state transfer between replicas, their number should be limited. In this paper we propose a self-healing solution that limits the number of group reconfigurations and ensures the availability of the replicated application in a dynamic environment. To evaluate the performance of our solution, we implemented it in a framework, called Semias, in the context of Vigne grid middleware. Experiments run on Grid'5000 and PlanetLab show the performance of the framework and the efficiency of our self-healing mechanisms in a dynamic environment.