Very good question. Let me write what I think here. However, NSs would help us understand this in a better way.
He works at night and sleeps during the day.
I think the word day took the definite article because here, in this context, a person's routine and time period is already defined in the first clause - he works at night. Probably, the day is definite as it follows the night described in that sentence.
Nocturnal animals sleep by day and hunt by night.
Adding the will make it "...animals sleep by the day..." which would mean something different.