We developed a Hidden Markov mark–recapture model (R package marked) to examine sex‐specific demography in Magellanic Penguins (Spheniscus magellanicus). Our model was based on 33 yr of resightings at Punta Tombo, Argentina, where we banded ~44,000 chicks from 1983 to 2010. Because we sexed only 57% of individuals over their lifetime, we treated sex as an uncertain state in our model. Our goals were to provide insight into the population dynamics of this declining colony, to inform conservation of this species, and to highlight the importance of considering sex‐specific vital rates in demographic seabird studies. Like many other seabirds, Magellanic Penguins are long‐lived, serially monogamous, and exhibit obligate biparental care. We found that the non‐breeding‐season survival of females was lower than that of males and that the magnitude of this bias was highest for juveniles. Biases in survival accumulated as cohorts aged, leading to increasingly skewed sex ratios. The survival bias was greatest in years when overall survival was low, that is, females fared disproportionality worse when conditions were unfavorable. Our model‐estimated survival patterns are consistent with independent data on carcasses from the species’ non‐breeding grounds, showing that mortality is higher for juveniles than for adults and higher for females than for males. Juveniles may be less efficient foragers than adults are and, because of their smaller size, females may show less resilience to food scarcity than males. We used perturbation analysis of a population matrix model to determine the impact of sex‐biased survival on adult sex ratio and population growth rate at Punta Tombo. We found that adult sex ratio and population growth rate have the greatest proportional response, that is, elasticity, to female pre‐breeder and adult survival. Sex bias in juvenile survival (i.e., lower survival of females) made the greatest contribution to population declines from 1990 to 2009. Because starvation is a leading cause of morality in juveniles and adults, precautionary fisheries and spatial management in the region could help to slow population decline. Our data add to growing evidence that knowledge of sex‐specific demography and sex ratios are necessary for accurate assessment of seabird population trends.