Knowledge of the life-history and population dynamics of Australia's iconic and evolutionarily distinct platypus (Ornithorhynchus anatinus) remains poor. We marked-recaptured 812 unique platypuses (total 1,622 captures), over four decades (1973-2014) in the Shoalhaven River, Australia. Strong sex-age differences were observed in life-history, including morphology and longevity. Apparent survival of adult females (Φ = 0.76) were higher than adult males (Φ = 0.57), as in juveniles: females Φ = 0.27, males Φ = 0.13. Females were highly likely to remain in the same pool (adult: P = 0.85, juvenile: P = 0.88), while residency rates were lower for males (adult: P = 0.74, juvenile: P = 0.46). We combined survival, movement and life-histories to develop population viability models and test the impact of a range of life-history parameters. While using estimated apparent survival produced unviable populations (mean population growth rate r = -0.23, extinction within 20 years), considering residency rates to adjust survival estimates, indicated more stable populations (r = 0.004, p = 0.04 of 100-year extinction). Further sensitivity analyses highlighted adult female survival and overall success of dispersal as most affecting viability. Findings provide robust life-history and viability estimates for a difficult study species. These could support developing large-scale population dynamics models required to underpin a much needed national risk assessment for the platypus, already declining in parts of its current distribution.