How long does it take for a destroyed rainforest area to recover?

There is no guarantee that it will ever recover. The layer of topsoil in a rainforest is extremely thin. Because there is so much competition for food in the forest, little material builds up to form topsoil. When the trees are cut down and the thin layer of topsoil is exposed to sun, wind, and water, it is more susceptible to erosion. When the topsoil disappears, the land becomes un-arable, and becomes essentially desert.