There is evidence of the benefits that breastfeeding (BF) provides to full-term and premature newborns who are hospitalized. In the latter, maintaining BF during and after hospitalization is difficult. Objective: To determine the factors associated with BF cessation in preterm infants one month after discharge from a neonatology unit. Patients and Method: Historical cohort of 218 newborns from the Very Low Birth Weight Newborn Follow-up Program of the Hospital Base Valdivia, hospitalized between January 2016 and June 2022 and who maintained BF at discharge. Biodemographic and clinical data were collected from available records and their relationship with BF cessation was evaluated one month after discharge. Results: One month after discharge, 35.8% of the infants abandoned BF (N = 78). The bivariate analysis highlighted a significantly lower median gestational age and lower mean birth weight in those who abandoned BF. Neonates born to married mothers, with a shorter median hospital stay and without requiring invasive mechanical ventilation had a lower proportion of BF abandonment. In the adjusted analysis, the educational level of maternal higher education was significantly associated with a lower probability of abandoning BF (adjusted OR: 0.3; 95% CI 0.11- 0.85). Conclusions: One month after discharge, over a third of the children stopped BF which was significantly associated with the mother's educational level. Support and educational interventions during hospitalization must consider the mother's educational background.