Let him sleep or try to wake him??

Hi my 6 weeks old LO sometimes fall asleep at night after half feed when he is suppose to drink a full feed. We usually let him sleep and when he wake again then feed again. But it sort of disrupt a schedule we trying to build into him and perhaps into our resting hours. Should I actually keep trying to wake him up and try to finish or just let him sleep. Letting him sleep is after trying for a while simple ways to try to wake him but fail. Did not bear to try harder. Thank you for your sharing in advance!