It takes a full term (40 week) pregnancy for the blood vessels which will supply oxygen to the retina to fully develop. The blood supply to the retina starts at the back of the eye at 16 weeks of gestation. The vessels gradually grow over the surface of the retina to reach the front edge at about the time of birth. When an infant is born early this process starts. There are a variety of reasons this occurs, but the most important ones in babies born today are the degree of prematurity and birth weight.
Once the blood vessels stop growing over the surface of the retina, a patch of retina ends up starved for oxygen. This leads to immature growth of retina.