To identify weaknesses in the continuity of care for preterm infants discharged from a neonatal unit, based on the perspective of professionals in the family health strategy. Qualitative research, carried out with 16 professionals from four health regions in a capital city in the center-west of Brazil. Data collection took place from October to December 2020, through semi-structured, individual, and in-person interviews. Data underwent content analysis, supported by the concept of continuity of care. The analysis consisted of three categories: Challenges for care in the unit and referral to specialized services; weak interactions between the preterm baby's family and health professionals; Information: essential aspect for the connection between health professionals and the family of the preterm newborn. Health services are shown to be fragile in terms of the dimensions of continuity of care, contributing to the discontinuity of care for preterm children.