Mom and infant . Babies get calcium from mom. Babies born at less than 32 wks gestation abruptly end their "supply" of calcium and it drops after they are born. Up to 70% of these bebies have this problem. Other causes are babies who have low apgar scores and have a low oxygen supply, preemies born to diabetic moms as they have a higher calcuim requirement, also moms with hyperparathyroidism and some seizure meds.
Lack of stores. Calcium, iron and protein stores are all obtained in the third trimester of gestation. If a child is shorted of this trimester by being born early then the stores are shorted as well. Add to this the fact that premies are often kept for days without being fed due to problems with their intestines thus delaying the time to fixing the low stores.
Many reasons. Hypocalcemia in newborns can be caused by maternal diabetes, medications, infection, periods of low oxygen delivery to tissues, and stress. All of these are more common with premature infants putting them at increased risk of hypocalcemia. Some genetic diseases may also cause low calcium levels. Newborns are not usually symptomatic, but sometimes may get jittery or even have seizures.