Here are a couple sites that have a lot of info on Zoysia grass.
http://www.empireturf.com
http://circlecfarmsinc.com/interacti...olving_1.shtml
I have been told that those dead spots are a result of not enough water early last summer and the grass was stressed, will take some time for it to recover. Also nematodes can also make the grass look dead like the brown out spots.
If there is a low growing pink weed in the dead area, nematodes can be the cause. I was told to put down milorganite
http://www.milorganite.com to supplement the soil to contain the nematodes.
Common Pests Of Zoysia Grass
Nematodes, mole and crickets are most problematic in the south along with grubs and billbugs in the rest of the growing areas. Pre-fumigating soils known to contain nematodes is the best option for controlling this pest with the addition of organic matter because nematodes grow best in sandier drier soils. Grubs and billbugs (moles and crickets in the lower South) are soil borne insects with can cause serious damage. Consult your extension agent for control recommendations. Early spring treatment for billbugs should be done when the first adults are seen. Contact garden centers with trained staff or county agents for insect diagnosis and control recommendations suggested. Be sure and read the label of any product you use.
Trying to grow grass in a sand box is a never ending challenge!