In my last question it was mentioned that it is the same Gannondorf returning, and a different hero of ages is chosen.
Why does this 'triforce' cycle keep repeating itself? Is there an in-universe explanation?
The short answer is: Because of Demise's Curse of Incarnation
As, I somewhat mentioned in my answer to that same question, the cycle of "Ganon" is referenced to the spirit of Demise resurfacing every so often.
You can watch the sequence that alludes to this here: Youtube Link
The short of it is that Demise is defeated for the first time by the Hero of Time with the Master Sword at the charge of the goddess. The spirit of despair manifested in Gannon will resurface, this is indicated somewhere in there.
It's a little vague, but the reasoning is that evil cannot be defeated and destroyed forever, but sealed, or put to sleep. It will resurface as many times as the franchise requires.
The Hero of Time is always chosen by the goddess, because if not, the world will be held by Ganon. Zelda's purpose is less clear, but perhaps she is simply the final piece of the puzzle, always.
The clip below shows exactly what happens and what is said to set the gears in motion. Go right to the end of it. Basically Demise, in his defeat is held by the curse of incarnation, explaining that the incarnation of his will, as well as the Hero of Time, and Zelda, will always be bound to conflict whenever he rises again (as Ganon).
End of Demise and His Curse
Just so it's clear, the people in this loop are:
Ganon (or the will of Demise)
Zelda (having the blood of the goddess)
The Hero of Time (chosen by the goddess each time)