Understanding the functioning of natural metapopulations at relevant spatial and temporal scales is necessary to accurately feed both theoretical eco-evolutionary models and conservation plans. One key metric to describe the dynamics of metapopulations is dispersal rate. It can be estimated with either direct field estimates of individual movements or with indirect molecular methods, but the two approaches do not necessarily match. We present a field study in a large natural metapopulation of the butterfly Boloria eunomia in Belgium surveyed over three generations using synchronized demographic and genetic datasets with the aim to characterize its genetic structure, its dispersal dynamics, and its demographic stability. By comparing the census and effective population sizes, and the estimates of dispersal rates, we found evidence of stability at several levels: constant inter-generational ranking of population sizes without drastic historical changes, stable genetic structure and geographically-influenced dispersal movements. Interestingly, contemporary dispersal estimates matched between direct field and indirect genetic assessments. We discuss the eco-evolutionary mechanisms that could explain the described stability of the metapopulation, and suggest that destabilizing agents like inter-generational fluctuations in population sizes could be controlled by a long adaptive history of the species to its dynamic local environment. We finally propose methodological avenues to further improve the match between demographic and genetic estimates of dispersal.