When do transformed creatures go back to their original forms?
Double-faced cards only transform when they (or another effect like Moonmist) explicitly say they transform.  For example, Ulvenwald Mystics says on its front side:

At the beginning of each upkeep, if no spells were cast last turn, transform Ulvenwald Mystics.

and the back side (Ulvenwald Primordials) says:

{G}: Regenerate Ulvenwald Primordials.
At the beginning of each upkeep, if a player cast two or more spells last turn, transform Ulvenwald Primordials.

Thus, the conditions for transforming in both directions are printed on the card.
Loyal Cathar, on the other hand, has a transformation-causing ability on its front side but no transformation-related abilities on its back, so once it transforms, it stays that way until it leaves the battlefield.