Does an aura fall off when its enchanted permanent becomes a different card type?

Auras have an 'enchant [quality]' ability that defines what they can legally be attached to. Whenever a state-based action check occurs, the game verifies that each Aura is still attached to a permanent that matches its enchant restriction (CR 704.5n).

If a permanent loses or changes its card type such that it no longer satisfies the Aura's enchant requirement, the Aura is put into its owner's graveyard as a state-based action. This is not the Aura 'falling off' as a triggered effect — it happens the next time state-based actions are checked, with no player receiving priority in between (CR 704.3).

Conversely, if the Aura's enchant restriction is broad enough to still be satisfied after the type change, the Aura stays attached with no problem. For example, an Aura with 'enchant permanent' will never fall off due to a type change, because any permanent satisfies it.

Concrete example: You have Rancor (enchant creature) attached to a creature. Your opponent casts Opalescence, turning all enchantments into creatures. Rancor itself becomes a creature, but the permanent it was enchanting was already a creature and remains one, so Rancor stays attached. However, if instead your creature were turned into an artifact with no creature type — for instance via a card that removes all types and makes it an artifact — Rancor would be put into your graveyard the next time state-based actions are checked, because it no longer enchants a creature.

The key rule references are CR 704.5n (Aura must be attached to something it could legally enchant, or it goes to graveyard) and CR 303.4c (an Aura attached to an illegal object is put in its owner's graveyard).