In the year 2015, more than one-third of neonatal deaths caused by prematurity was recorded worldwide. Despite different kinds of efforts taken at the global and local levels to reduce neonatal mortality, it remains high with low reduction rates, especially in low- and middle-income countries like sub-Saharan Africa and South Asia. Therefore, this study aims to assess the survival status and predictors of mortality among preterm neonates. A retrospective follow-up study was conducted on randomly selected 561 preterm neonates. Data were extracted from patient records using a pretested checklist. Data entry and analysis were done using Epi-Data Version 4.4.2.1 and Stata version 14, respectively. The Cox proportional hazard regression model was fitted to identify the predictors of mortality. A hazard ratio with a 95% confidence interval (CI) was estimated and p-values < 0.05 were considered statistically significant. The proportion of preterm neonatal deaths was 32.1% (180) with an incidence of 36.6 (95% CI: 31.6-42.4) per 1,000 person days. The mean survival time was 18.7 (95% CI: 17.7-19.9) days. Significant predictors for time to death of preterm neonates were respiratory distress syndrome [adjusted hazard ratio (AHR): 2.04; 95% CI: 1.48-2.82], perinatal asphyxia (AHR: 2.13; 95% CI: 1.32-3.47), kangaroo mother care (AHR: 0.14; 95% CI: 0.08-0.24), and gestational age (AHR: 0.85; 95% CI: 0.80-0.90). Preterm neonatal death is still a major public health concern. Respiratory distress syndrome, perinatal asphyxia, kangaroo mother care, and gestational age were independent significant predictors for time to death, as found in this study. Hence, priority must be given to neonates with the above illnesses and strengthen the management and care of preterm neonates.