I actually had a cake order that I had this problem with. Several years ago, I did a 2 tier cake for a July bridal shower. Unfortunately, I thinned my icing a little to much for the humidity in my area....I glanced in the dining room where the cake was sitting, already decorated, and was I surprised....the icing on the bottom tier had slid down the sides and making the top tier lean! I learned my lesson from that cake...I make sure my icing is "thicker" for the hot, humid months now. Fortunately, I was able to scrape off the icing and re-do the cake so that it wasn't a total loss.