Understanding the mechanisms underlying population declines is critical for preventing the extinction of endangered populations. Positive feedbacks can hasten the process of collapse and create an 'extinction vortex,' particularly in small, isolated populations. We provide a case study of a male-biased sex ratio creating the conditions for extinction in a natural population of tuatara (Sphenodon punctatus) on North Brother Island in the Cook Strait of New Zealand. We combine data from long term mark-recapture surveys, updated model estimates of hatchling sex ratio, and population viability modeling to measure the impacts of sex ratio skew. Results from the mark-recapture surveys show an increasing decline in the percentage of females in the adult tuatara population. Our monitoring reveals compounding impacts on female fitness through reductions in female body condition, fecundity, and survival as the male-bias in the population has increased. Additionally, we find that current nest temperatures are likely to result in more male than female hatchlings, owing to the pattern of temperature-dependent sex determination in tuatara where males hatch at warmer temperatures. Anthropogenic climate change worsens the situation for this isolated population, as projected temperature increases for New Zealand are expected to further skew the hatchling sex ratio towards males. Population viability models predict that without management intervention or an evolutionary response, the population will ultimately become entirely comprised of males and functionally extinct. Our study demonstrates that sex ratio bias can be an underappreciated threat to population viability, particularly in populations of long-lived organisms that appear numerically stable.