An age-structured demographic matrix model is developed to determine the long-term viability of the Southern African Kgalagadi Transfrontier Park lion (Panthera leo) population that is subjected to persecution along the park boundaries. In doing so, maximum sustainable persecution rates are established, so that efficient conservation measures may be taken, if required, to ensure the continued survival of the species in the park. Sensitivity analyses indicate that adult female survival ability alone is the most important component of the model in terms of long-term population survival. Furthermore, these analyses show that the boundary prides of the park are able to increase their chances of survival and are able to sustain significantly higher human-caused mortality rates by inducing birth-sex ratio biases in favour of females. The model suggests that the persecution rate experienced by the study population over the period 1998–2001 cannot be sustained in the long term, provided that there is no immigration of adult females into the population from the park interior. To ensure the survival of existing park boundary prides, adult lionesses should, as far as possible, be afforded protection from persecution, so that park boundary populations do not merely serve as population sinks for lions from elsewhere, or become extinct.