My blind bags are always taking a tumble. For the longest time, when I had all my CP ponies lined up on the top shelf of my main pony display, the cats would like jumping up there and knocking them down. Oddly enough, I changed it out to display the Dream Castle, Majesty and the Princesses and now they leave it alone!
I'm just glad they don't chew ponies; there are quite a few on floor level...