It could be grubs. (Japanese beetle larvae) If it is, buy grub killer granule and put it down over entire lawn. Your lawn will repair faster if you remove dead zoysia and put seed down. (Now is the time of year to repair any spots that are sparse or dead. But not treating the reason it became sparse or dead FIRST will cause damage to keep reoccurring.)
I don't I know if I have the Cure but I may have an answer to why. My lawn professional told me it was because there was a virus going around that was attacking zoysia grass. Mine is almost non-existent now. So perhaps a good dethatching and fresh plugs may help the problem.
You should check with the center for home gardening inside the MBG
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