Feeding 1 month old during night

Hello mummies, my 1 month old baby kept falling asleep after drinking about 60ml at night. Usually she will take about 100-110ml during the day. I tried my best to wake her up after she drank the 60ml to finish the remainder 40ml from bottle but she just wouldn’t continue drinking it. Is it ok to let her back to sleep or should I continue to try harder? Thanks in advance (: