Engine stops after running a bit

I think it is a FD750D I know its a 27hp Kawasaki in my Simplicity Mini Tractor with 1k hrs, It's 3:30 am and am not going outside to verify right now. I've Goggled till I cant Goggle anymore. I was going to change the coils next but I do not think both would go quit working at the same time.When it quits running it's like the key was turned off. It will run for 10 minutes when cold, (runs great), let it sit for 5 minutes restart and runs great for a couple minutes. It will die at full throttle with the blades engaged and when just trying to baby it back to the garage. I've done all prelems, Vent on gas cap (even ran it loose) new fuel filter (clear with fuel flow), new pump (working to carb) new battery (all connections are clean) (I haven't check the engine ground I guess that's next but does not make sense). New plugs (looking good but only have 20+ minutes on them. Oil and filter newer (10 hrs) and level good. Someone please help. I've got 7 acres of 12" high grass and weeds to mow.

Thanks for the thought. Narrowing down the issue. I thought I had been doing that. But with that said your recommendations narrows it down to electrical (where or what). or fuel yes. if it starts up and keeps running its a carb issue. It just does not seem like a carb issue because of the way it stops running.
 
It just stops, So I am thinking it is an electrical issue.
 
So if it is electrical (considering what I have already done) where would you go from there?
 
Thanks in advance for your response.

Bart
Thanks for the thought. Narrowing down the issue. I thought I had been doing that. But with that said your recommendations narrows it down to electrical (where or what). or fuel yes. if it starts up and keeps running its a carb issue. It just does not seem like a carb issue because of the way it stops running.
 
It just stops, So I am thinking it is an electrical issue.
 
So if it is electrical (considering what I have already done) where would you go from there?
 
Thanks in advance for your response.

Electrical and fuel stalling can sound / do, exactly the same thing.  
 
You HAVE TO check for spark when it dies.  You HAVE to confirm if there's spark or not.  
 
Your second guessing and jumping forward W/O confirming basic's first...
 
.
 

For anyone that is interested, replacing the items mentioned above fixed the problem. even though the engine had what I thought was one issue, I believe there were multiple issues not just one. I have had over 20 hours on it now running very well.