I've got a roughly 11yr old Deere Z925A Zero Turn with a Kawasaki FX751V on it. The motor runs good and strong, but never wants to restart after it's up to operating temperature. I've changed the coils and rebuilt the carb. Neither of those have corrected the problem. There's a fuel shutoff solenoid on the back of the carb that's been checked as well, and it's functioning as designed. I'm officially out of ideas! Has anyone experienced this before?
I see where you've changed the coils but you need to do basic diagnosis to see why it isn't starting when this happens.
I assume it's cranking over but not running?
Then the first thing would be to determine whether it's not running because it has too little fuel or too much.
Technically you can claim it has too much fuel if it has no spark because the plugs are wet but regardless that's the things, it either doesn't get enough fuel to run or it could possibly have too much but that should be more obvious or it doesn't have any spark as it's cranking over.
I think the fastest way to determine this is to take the air filter off and spray a little bit of carb cleaner in it when it won't start and see if it hits or even just add some choke.
I have found a lot of Kawasakis that simply don't like to start when they're hot unless you give them choke for 3/4 of a second to a second. Then they fire it up.
If you don't give them choke they will sit there and spend over 8 to 10 times before they fire up sometimes never doing it.
So go back to the basics on square One and see if adding some fuel IE carb cleaner into the intake with the choke open when you spin it over causes it to fire up. If not then you need to check for spark.