I put fondant cakes in the fridge every week and I don’t have any problems. There will be some condensation upon removing it, but in an hour the fondant will dry right back out. I have in the past, put a garbage can liner over the cake and taped the opening to a cake board (think of it as a ghost costume for the cake. Put the bag on before the cake is cooled, remove it just as you take the cake out of the cooler and I have 0 problems with condensation.
To answer the actual question though I think depends on the type of icing underneath that fondant. I think ganache or shortenin based buttercreams would last longer than other icings.