Does protection from a color prevent auras of that color from falling off or just from being newly attached?

Protection from a color does two relevant things regarding Auras: it prevents new Auras of that color from being attached to the protected permanent (the 'A' in DEBT — Attached), and it also causes any Auras of that color that are already attached to fall off immediately as a state-based action.

According to CR 704.5n, state-based actions are checked continuously. One of those checks is: if an Aura is attached to an object it can't legally enchant, the Aura is put into its owner's graveyard. Since a permanent with protection from a color can't legally be enchanted by an Aura of that color (CR 702.16b), any such Aura already on it will be moved to the graveyard the next time state-based actions are checked — no spell or ability needed.

CR 702.16b defines protection as preventing the permanent from being 'enchanted' by sources of that quality, which covers both the attachment step during casting/resolving and the ongoing legality of existing Auras.

Concrete example: Your creature is enchanted with Unholy Strength (a black Aura). Your opponent targets it with a spell that gives it protection from black. As soon as that effect resolves and state-based actions are checked, Unholy Strength is immediately put into its owner's graveyard — it doesn't stay on just because it was already there.

So in summary: protection is not just a 'shield against new attachments.' It retroactively invalidates existing Auras of the protected color too, causing them to fall off via state-based actions.