Hair loss. It is normal for infants to lose hair in the first 4 to 6 months of life, or not to have much in the first year at all! A bald patch along the back of the head can also occur when the baby rubs his scalp against the mattress. Due to the importance of the back sleeping position in the prevention of SIDS, changing sleep position is not recommended. The hair regrows eventually. If your baby still has not grown hair by 12 months, talk to your pediatrician.