So while a character in fiction my create what appears to be a stable time loop, it is merely a part of a long progression of loops connecting parallel universes. The object has ceased to move down the timeline vertically with everything else, it's moving horizontally. Eventually the object will degrade and things will be done differently but not in the universe covered by this specific story you are reading/watching/whatever.
Take Ocarina of Time's Song of Storms for example. The song is first learned in where the windmill guy in Kakariko teaches Adult Link the song. Adult Link then goes back into the past and, as Young Link, teaches the song to the guy in the windmill, causing the time loop. However, it can be said that this all began when another boy with an ocarina (let's call him Bort) learns the song from the Composer Brothers, then teaches it to the windmill guy - not a paradox. The windmill guy then teaches the song to Adult Link. This causes a timeline break where the kid who teaches the song to the windmill guy changes from Bort to Young Link, beginning the loop and possibly removing Bort from the timeline.