The donkey breed Asinina de Miranda, with fewer than 1000 breeding females, is in danger of extinction. The objectives of this study were to predict the progression of the breed under present management and identify determinants for survival, by means of a population viability analysis program, in order to suggest suitable management strategies. The simulation showed a high risk of extinction. The most critical factor for breed survival was the percentage of females breeding per year, but the actual percentage needed depended on the carrying capacity of the breed. Reducing female mortality and age at production of first offspring, assuring registration in the Studbook, and tracking the foals will significantly foster this donkey breed’s recovery and maintenance. The breed comprised a potentially reproductive population of 589 individuals; however, just 54.1% of the adult females registered in the Studbook ever foaled, and of these 62.7% foaled just once. The overall neonatal mortality for the first month of life was 8.92% and was lower in females (6.51%) than in males (12.0%) (P = 0.028). Neonatal mortality was unevenly distributed throughout the year, with lower mortality rates recorded in February–May and October–November, and higher mortality rates in June–September and again in December–January. The neonatal foal mortality rate was lower with females aged 5–15 years (8.06%) than those younger than 4 years (10.3%) or older than 16 years (14.1%) at foaling.