Here's one: Final Fantasy IV (or II is the US). When you are trying to get Rydia out of the village you just burned, she summons Titan, which causes a massive earthquake. But soon afterward, Rydia joins your party and cannot summon Titan, nor does she gain the ability to do until much later in the game.

The only explanation I have ever heard for that which makes some sort of sense is that she simply called out in desperation to any Eidolon and Titan answered her call.