Vultures in Africa are being poisoned deliberately by poachers to prevent the birds alerting authorities to the poachers’ illegal activities, or for harvesting and sale of body parts for use in witchcraft. Hundreds of vultures can be killed at a single poisoned elephant Loxodonta africana carcass, and although field staff trained in poison response activities can limit the damage, mortalities remain numerous. We used the population viability analysis programme VORTEX to simulate seven 100-year-long scenarios investigating various rates of poisoning mortalities and the remedial effects of poison response activities on a population of Critically Endangered white-backed vultures Gyps africanus breeding in Kruger National Park, South Africa. In six scenarios the population declined (λ < 1); in three scenarios the population remained extant over the 100-year simulations but declined by 60–90% from a starting size of 2,400 individuals. In two scenarios one poisoned elephant carcass left untreated and causing the greatest number of vulture deaths was modelled as a catastrophic event with a 50% probability of annual occurrence, which resulted in a 100% probability of population extinction, with a mean time to extinction of 55–62 years. Effective poison response activities were modelled as a 70% reduction of mortality at each poisoned elephant carcass and resulted in population persistence after 100 years but with a c. 90% reduction in size (final n = 205). We highlight that although poison response activities will not prevent poisoning from occurring, they form an essential part of wider conservation actions designed to prevent local extinctions of vultures or other vulnerable species.