Don't worry!! As the midnight till to morning time, they are too tired to drink, for my baby, it is normal. I think your baby will quit the night time milk very soon. my baby now is 3 months old, she is already quit the night time milk. When she was new born till now, she is keeping breastfeeding between 3 to 4 hours. You do not need to worry about, she is OK! If you still are worrying, you could ask the doctor.