I am trying to cover a cake board with fondant, and it's just not working! I used some BC to get it to stick, wraped it around "butt-cut" the corners. and used BC on the bottom (for stickage) it's TOO soft, keeps falling off....in other words a complete disaster! Help!!! 
I prefer to only cover the TOP of my board with fondant, cutting it flush with the edge of the board, then trimming off the edge with ribbon. I think it gives it a nicer look
Here's a closeup of how it would look (SIGH I soooooooooooooooo can't wait until my website is finished so I can just show links to my pics lol).
Sounds frustrating - sorry you are dealing with this!
You may want to try just using a very light coating of shortening on your board instead of buttercream. Your fondant doesn't need much to stick to.
Also, not sure why you are wrapping it on the bottom. Maybe just do a clean cut around the bottom of the board. Or take the fondant to the end of the board and add a nice ribbon - just my opinion, but I think this looks much better than wrapping the whole board.
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