There is no one definitive answer to this question. Some people say that broken capillaries on the face do eventually heal, while others claim that they do not. Factors that may influence whether or not a broken capillary heals include the severity of the break, how long it has been since the break occurred, and the individual’s overall health and age. If you are concerned about a broken capillary, it is best to speak with a doctor to get their professional opinion.