Globally, the African wild ass (Equus africanus) is at risk of extinction in the wild. Major threats to its survival are hunting, competition with livestock, and interbreeding with the domestic donkey. An important but rare population exists on the Messir Plateau in the Danakil ecosystem of Eritrea. Long-term data on reproduction and survival rate of African wild asses are limited, making it difficult to predict the population trend. Therefore, we assessed the population's potential viability given certain assumptions. An age-structured matrix model was used to project the population growth rate generated by assumed vital rates. The probability of population persistence over 50 years was estimated allowing for stochastic dynamics, density dependence, influences of rainfall on carrying capacity, and episodic disturbances reducing survival rates. Scenarios used either historical rainfall patterns or potential future rainfall with the same or amplified coefficient of variation. We contrasted two estimates of carrying capacity based either on recent population assessments, or on the potential capacity of the study site. Our models also compared realistic versus optimistic scenarios for age at first reproduction and potential longevity. The probability of persistence of a population of 18 females was reduced to < 50% in the worst-case scenario. With a potential carrying capacity of 37 females, persistence was projected to be almost 100% under all scenarios. The greatest threat to population viability seems to come from livestock impacts on the resources that limit the African wild ass population size under anticipated climate change scenarios. Further studies are required to assess the level of competition between African wild asses and livestock to guide effective conservation strategies