Help! Gator with Kawasaki engine quits after warmup

I have an early 1990's Gator AMT 626 that has started an odd problem that results in the engine dying after it has warmed up for awhile. It will not restart until it has sat for a bit and cooled off. Then it starts and runs and warms up and dies again, etc. Could an ignition coil or something be failing? The dying is getting more frequents after warmup.

Thanks for your advice.