Variation in disease incidence in wildlife is often assumed to reflect environmental or demographic changes acting on an endemic pathogen. However, apparent endemicity might instead arise from spatial processes that are challenging to identify from traditional data sources including time series and field studies. Here, we analysed longitudinal sequence data collected from rabies virus outbreaks over 14 years in Costa Rica, a Central American country that has recorded continuous vampire bat-transmitted rabies outbreaks in humans and livestock since 1985. We identified five phylogenetically distinct lineages which shared most recent common ancestors with viruses from North and South America. Bayesian phylogeographic reconstructions supported bidirectional viral dispersals involving countries to the north and south of Costa Rica at different time points. Within Costa Rica, viruses showed little contemporaneous spatial overlap and no lineage was detected across all years of surveillance. Statistical models suggested that lineage disappearances were more likely to be explained by viral extinctions than undetected viral circulation. Our results highlight the importance of international viral dispersal for shaping the burden of rabies in Costa Rica, suggest a Central American corridor of rabies virus invasions between continents, and show that apparent disease endemicity may arise through recurrent pathogen extinctions and reinvasions which can be readily detected in relatively small datasets by joining phylodynamic and modelling approaches.