It is actually quite common for young babies to sleep through the night and not want to nurse at night. My friend's baby went through the same thing and what my friend did was to increase baby's nursing time in the day. She fed baby once every 2 hours instead of the previous 3 and she "tanked" baby with milk before bedtime. Baby sleeps through the night and there is no worry if baby is under-fed.
Also, try to minimize any distractions when feeding baby in the day. Babies usually get distracted by so many things as her surroundings are more lively in the day thus causing her to drink less milk. Nurse baby in a quiet and slightly darkened room if possible.
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