Discovering latent dependence structures over the nodes of a dynamic network is a difficult challenge that is of increasing importance in many applied fields. Our interest is motivated by a demographic analysis of the complex interaction between causes of death in the Italian population observed on a fine age grid. To unveil non-trivial grouping structures between causes of death, we rely on a simplified version of a recently proposed stochastic block model for dynamic networks [4], which is able to learn node partitions having common connectivity patterns. To flexibly account for the time evolution of the node grouping structure, such a model relies on a dynamic random partition process, which permits to learn sequences of partitions with a high and evolving level of persistence over time.