In Poe's "The Tell-Tale Heart," it may be that the narrator does not kill the old man during the day because he cannot abide to look at the eye.
It is impossible to say how first the idea entered my brain; but once conceived, it haunted me day and night. Object there was none. Passion there was none. I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire. I think it was his eye! yes, it was this! He had the eye of a vulture—a pale blue eye, with a film over it. Whenever it fell upon me, my blood ran cold; and so by degrees—very gradually—I made up my mind to take the life of the old man, and thus rid myself of the eye forever.
The narrator is clearly insane: he admits that he has no reason to kill the old man other than his eye. His description of the eye personifies it into a living thing, separate from the man, for he is aware that the old man has done him no harm. He does feel, however, threatened by the eye. He describes it as an eye much like that of a vulture. The association with these birds is death because they are scavengers that often survive by eating dead things—such as animals killed on the road or the carcass of another animal's kill.
Their eyes are wide and often seem to bulge. The narrator's mind has erroneously conceived that the eye itself is a threat to him.
The fact that the speaker describes the eye when it is opened would lead us to presume that he will feel less threatened if he kills the old man when he is asleep and his eye is closed. Although the white film on the eye indicates that the eye is incapable of sight, the danger in the narrator's mind may be in his perception of being seen by the eye—even though the eye cannot see.
Of course, the other reason he kills the old man at night is because he wants his actions to go unnoticed. Generally speaking, few people would be up and walking about on the streets or awake in their homes at such a late hour, limiting the number of potential witnesses to any suspicious sounds emanating from the house during the murder.