I did this two years in a row. The first year I put down a thin layer of topsoil not covering the grass. That helped a little. The following year I had the same weak spots. This time I put down a heavy layer of topsoil, up to just the tips of the grass. This did wonders to the weak areas and they have stayed ok for the past year. Water the topsoil in after applying.
I believe all our problems would go away if it would rain more than once a month.....................
Here are a couple helpful websites;
Circle C Farms - Interactive Problem Solving
Central Florida Sod Farm | Lake Jem Farms
EMPIRE Turf | Zoysia Grass | One Lawn, Many Benefits