Learn Russian: Это ошибка, из-за которой я сутками не сплю. - This is a mistake because of which I don't sleep for days on end.

This is the bare instrumental of extended duration. When a time noun is used in the instrumental plural (like сутками, часами, годами), it means the action happens continuously for that period on end. Here, it translates to "for days on end."

Could I use днями instead of сутками to mean "for days"?

You could, but сутками is much more precise and natural here. Сутки specifically refers to a full 24-hour period of day and night. Since the speaker is talking about an inability to sleep, сутками perfectly emphasizes that they are awake around the clock.

Why use из-за которой instead of just потому что?

Потому что is a conjunction that connects two independent clauses (e.g., "I don't sleep because I made a mistake"). However, this sentence uses a relative clause to describe the noun ошибка. To say "a mistake because of which," you need the preposition из-за followed by the relative pronoun который. It becomes которой to match the feminine noun ошибка and to take the genitive case required by из-за.

Why use the preposition из-за for "because of" instead of от?