When making cupcakes, I like to use fondant cutouts for decoration. Mainly, I use circle cutouts with an initial monogram. Both times I've done this, it's like the fondant starts to disinegrate once placed in the fridge, and becomes gooey and slides off the cupcake. Is my only option to wait as long as possible before placing the circle on top of the cupcake?

Fondant does best at room temperature. The cooling of the fridge and rewarming to room temperature causes condensation which can break down the fondant. If you have to put the cupcakes in the fridge because of a filling or something, definitely wait to put the fondant on!

moisture is the enemy of fondant. Don't put them in the frig. All frigs are moist - especially frost free ones.