I have recently tried my hand at stacking tall cakes.  My last two cakes have been so big that they don't fit in my fridge.  So I decided to leave them out after covering them with fondant.  What has happened is that the cakes have gotten soft and the fondant has melted.  Consequently, I've ended up with lopsided cakes and sagging fondant.   I don't think I have to describe the feeling to my fellow cakers when you see your cake leaning after you've been in so much working into what you thought was a piece of art!  At first I thought it was because I've been making my own fondant but now I'm thinking it's because I didn't refrigerate the cakes after covering them.  If the cakes depend so much on cool temperate then will same thing happen if they sit at the venue for too long?  Is there any way to keep this from happening?  

I don't work much with fondant, usually just buttercream, but I have always heard that fondant covered cakes should not be refrigerated anyway. It sounds like your problem is with what is under the fondant. What kind of icing are you using under the fondant?

Thank you for the reply.  I used chocolate ganache under the fondant and the filling was caramel coconut cream, but I made sure not to overfill it because I didn't want any bulge.  

I actually always refrigerate my fondant covered cake, there are some tricks you can use to avoid the sweating issue.  What kind of dowels are you using to support your tiers?  How far apart are you spacing them and how many are you using.  Also, what kind of cake board are you using on each of your tiers?  Do you use buttercream under the fondant, if not what do you use?  And what is the temp like in your area.  All of these questions will help people to understand what could have happened.  And if you have a picture of the cake that would also help.

I used wooden dowels and placed five for a 6 in. cake and five again for a ball cake on top with one long dowel going through  the ball.  The cake boards were cardboard.  All the dowels were spaced one inch from the edge of the cake placed on top.  The temp in NY yesterday was 65 degrees but the car was warmer.  It started to lean as the car began to hit bumps.   I used ganache under the fondant and coconut butter cream for the filling.  Should I have used ice packs for the transport?  Here is a picture.  Sorry its not very good.  The cake looked so bad I couldn't bring myself to take a close-up.  

Its hard to tell but it looks like the problem lies with the bottom tier.  First it looks like that middle tier was not placed directly in the middle of the bottom tier (it looks like there is more room on one side as opposed to the other side).  You support system seems fine and I use the same kind of dowels but I would never transport a fully assembled 3 tiered cake.  I think if you would have not stacked it to begin with and where able to put it in the fridge to cool and set up which would make it so much easier to transport then assembled at the venue there would be no problems. The problem with using the wooded dowels with a unrefrigerated cake stacked is that they can easily slip just due to the icing softening up.  Then throw in the transporting it unrefrigerated and stacked and it could slip even more which could cause the leaning affect or worse.  So my advice is to stack on site and refrigerate each tier. 

ADid you try to stack the fondant cakes immediately after covering?

No I actually waited until the fondant was set before stacking the tiers.  

Thank you so much for all the advice, reginaherrin.  Its extremely helpful!  Good to know there are experts like you out there!