They're both correct, but both are normally used in describing a general (recurring) activity, rather than a specific one-time (single) task. The first one focuses on the length of the days, the second one on the succession (number) of the days. That is, in "day after day," you might devote only a half hour to the task each day.
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New2grammarThanks, Avangi. Also, is the and in day in and day out optional?Technically, it should be there, but almost nobody says it that way. I'm not sure I've seen it in written form.
New2grammarThanks, Avangi. Also, is the and in day in and day out optional?My experience comports with Philip's position, but I might not put it so extremely. I know a song, "Day In Day Out," and I know another song "Day In And Day Out." (I guess the first one is really "Thinking Of You.")