Kohler sh265 ARGGGHHH!

I have a this engine on a County Line log splitter.  A month ago, it started having issues.  It would start and run well for a few minutes and then simply die.  Would start right up again, but once more only run, albeit well, for a minute then die.  I pulled and cleaned the carb, checked the float, jets and needle valve. Re-installed.  Same issues.  Then I drained and cleaned the tank thinking that debris was periodically clogging the filter.  Re-installed after adding a new filter and fuel line.  It started right up but same issue.  I then thought coil and/or the plug.  I replaced both, which included a new plug wire as well.  Same problem.  Okay, maybe an air leak.  I had a new carb on hand with new gaskets, so I replaced the carb and intake gaskets.  Same problem.  I am at wits end here.  It starts easily, runs well for a few minutes, then dies.  HELP its cold and I've split enough wood by hand!

I'd pull the bowl (still installed) and make sure fuel IS flowing out of it.
 
I would also loosen the fuel cap to make sure the tank is vented
(and not running out of fuel with a full tank).
 
Check for spark, looking at the spark plug WHEN IT DIES..
 
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Just cause parts are new does not mean their good.
 
"I'd pull the bowl (still installed) and make sure fuel IS flowing out of it."  Did you do this??
 
 Make sure the coil is installed correctly-They often have stamped in them "up".
 
Check spark (with the new parts) and rule it good or not. 
Coil failure will OFTEN work, then loose spark after getting warm/hot.
 
An air filter will not shut down an engine after a certain amount of run time,
UN-less the loss of air flow fouls the spark plug.
 
Valve clearance / adjustment is easy.  With the intake valve open, check the exhaust clearance.
Likewise, with the exhaust valve open, check the intake.   I doubt this is the issue but should be checked