Private baptisms are carried out when the child is not expected to live.. The belief was (and I believe still is in the catholic & Cof E churches) that even an unbaptised baby could not be admitted to heaven. During my confirmation classes in about 1950 we were taught that in an emergency anyone could carry out a baptism and midwives especially were expected to do this. The fact that the child was received into the church several years later means that in that case there was a happy ending.