Babies can develop sleep apnoea. There are mainly two types, obstructive sleep apnoea and central apnoea. Some children develop obstructive sleep apnoea when they develop upper airway obstruction where they tend to snore, restless during sleep, they make snorting noises with mouth open. They can pause their breathing for seconds and then toss and turn in sleep or half wake up and go back to sleep. These things tend to improve as they get older. Intervention and investigation like sleep study if the episodes are prolonged, recurrent with colour change ie cyanosis etc. Acid reflux can cause apnoea in small babies. Most apnoeas will resolve spontaneously, some need stimulation. If it is acid reflux they baby can go red in the face. Does he change colour like going blue during this episodes and how long (seconds) does he stop breathing. It is worth recording these episodes on video, so the doctor can see what he is doing during the episode. You are right in seeking a doctor s opinion.