It sounds like a bad coil
Check the oil level,it has a low oil shutdown switch you could have a leak..old oil or oil with water in it will cause it too,change the oil and fill to line on stick.
Had a similar problem and it was a fuel issue. But, it could be electrical as well.
You would have to check fuel flow and for spark when it fails.
One possibility is the fuel filter is clogged (when was the last time it was changed?) and after it sits for awhile enough fuel gets through the filter and between what's on the output side of the filter and what is seeping through it runs for some time then quits.
It could also possibly be some crud in the float bowl of the carburetor that drifts around then clogs the float valve starving the engine of fuel then when it stops and the fuel fills the bowl again the crud drifts away from the valve to start the process over again.
Do a search for Kawasaki and your engine model and manual and you'll find a free downloadable manual which might be helpful.
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