Looks like that bottom piece is made of particle board
http://www.homedepot.com/p/5-8-in-x-...5302/204996444 and the sides are made of plywood.
Particleboard is a waste-wood product that is made by mixing sawdust with adhesives. Although it will not bow or warp like plywood, it can swell and become unstable when exposed to water.
quote taken from Lowe's website.
In my experience, once particle board is broken it continues to break down. Removing the legs would not resolve the problem. The only fix is to replace the board.