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It lasts permanently (as long as it's enchanting the creature). It simply states something which is true, so it will apply to all untap steps (of the creature's controller), not just the following one.
"Enchanted creature doesn't untap during its controller's untap step." is a static ability.
113.3d Static abilities are written as statements. They’re simply true. Static abilities create continuous effects which are active while the permanent with the ability is on the battlefield and has the ability, or while the object with the ability is in the appropriate zone. See rule 604, “Handling Static Abilities.”
So the rule-modifying continuous effect it creates will last until the Charmed Sleep leaves the battlefield.