Seasonal tropical environments are among those regions that are the most affected by shifts in temperature and rainfall regimes under climate change, with potentially severe consequences for wildlife population persistence. This persistence is ultimately determined by complex demographic responses to multiple climatic drivers, yet these complexities have been little explored in tropical mammals. We use long-term, individual-based demographic data (1994 to 2020) from a short-lived primate in western Madagascar, the gray mouse lemur (
Microcebus murinus
), to investigate the demographic drivers of population persistence under observed shifts in seasonal temperature and rainfall. While rainfall during the wet season has been declining over the years, dry season temperatures have been increasing, with these trends projected to continue. These environmental changes resulted in lower survival and higher recruitment rates over time for gray mouse lemurs. Although the contrasting changes have prevented the study population from collapsing, the resulting increase in life-history speed has destabilized an otherwise stable population. Population projections under more recent rainfall and temperature levels predict an increase in population fluctuations and a corresponding increase in the extinction risk over the next five decades. Our analyses show that a relatively short-lived mammal with high reproductive output, representing a life history that is expected to closely track changes in its environment, can nonetheless be threatened by climate change.