I think it is very unusual to see apnea while breastfeeding in 37 wk babies.
I do see term babies and preterm babies that do not coordinate their
suck-breathe-swallow. When you observe the feed you will see the baby do a
suck-suck-suck-suck- then pant, pant,pant and he or she may turn blue. The
treatment is to pace the feed, breaking suction every 2 sucks. I would also
rule out a swallowing and cardiac problem. Marjorie Palmer has written an
article on the Transitional Sucking Pattern, or immature sucking pattern that
describes this type of feeding.