At the beginning of each upkeep, if enchanted creature is untapped, tap it.
6/15/2010 Narcolepsy’s triggered ability has an “intervening ‘if’ clause.” That means (1) the ability triggers only if the enchanted creature is untapped as any player’s upkeep begins, and (2) the ability does nothing if the enchanted creature is already tapped by the time it resolves.
6/15/2010 Narcolepsy doesn’t keep the enchanted creature continually tapped. The creature untaps during its controller’s untap step as normal, then is tapped when Narcolepsy’s ability resolves during that upkeep. The creature may be tapped in response (for example, if it has an activated ability with in its cost).