Level 1: Reasons why a five-month-old baby does not eat milk. If a five-month-old baby does not eat milk, it may be due to the following reasons. First, your baby may be growing teeth, which can cause discomfort in their mouth and interfere with eating. Secondly, the baby may feel uncomfortable or sick, which can also affect their appetite. Finally, if the mother feels nervous or anxious while breastfeeding, it will also affect the baby