In this paper we present an analytic study of the impact of churn in cluster-based overlay networks. Cluster-based overlays keep the best of unstructured and structured overlays in terms of scalability, fault-tolerance and stability. Most of join and leave events have no impact on the overall overlay topology making these overlays highly robust to high churn. The only situations that effectively give rise to topology modifications are when clusters need to split because they exceed some maximal size or need to merge because they fall under some minimal size. Although these operations are scalable, they are intricate in the sense that they need synchronization among nodes involved in these operations. In this paper we accurately predict the frequency at which the topology of the overlay changes according to the number of join/leave operations. Our analysis improves upon existing studies by showing that these relevant topological changes are very infrequent, namely $\Theta(N)$ join/leave events are required before any of these topological operations occur, where $N$ is the number of peers currently in the system. Such a result clearly demonstrates the appropriateness of these overlays to high churn.