I refrigerate all my cakes too, fondant or not. There can be issues with condensation, but I have found that it you don’t touch it – it will dry out and look fine. I think the part that worries me the most is your comment about the cake collapsing… are you supporting your tiers properly?
FYI – I’m in the USA in GA (the Deep South) and our humidity is crazy bad from June through August
Jenniffer White, Cup a Dee Cakes - http://cupadeecakes.blogspot.com