First: Check where the throttle cable is clamped to the engine. If that clamp is loose, the throttle housing will move instead of just the wire inside. Remove the engine cover, and check for grass, dirt, mouse nest, and various other things in there that will block the flow of cooling air for the engine! Check gas cap for a bug nest in the breather hole. Check the air filter for being really dirty. Install new spark plug. And, carb may be dirty inside, A good soak in cleaner and a blow-out of all passages would probably help. check your gas can for water condensation inside of them. It does happen! A bit of Dry-gas in the tank does wonders. There is a funnel available that takes any water out of the gas when you pour it into yer tank. Can't remember the name-somebody here will know it.

Check vent in fuel cap. New fuel filter. Make sure seat switch is fully plugged in and adjusted to insure good plunger travel. Another possibility is the fuel pump is weak. A restricted filter or weak pump may result in enough fuel flow when NOT under load, but allow the carb bowl to slowly run out of fuel when under load. You might also check the quality of spark with a cold engine and again when the problem occurs. You may have a heat sensitive coil(s). IF so, cleaning the cooling fins might make a difference. This post was edited by bill_kapaun on Sat, Jul 26, 14 at 21:48

did you release the hydro relesae valve?? the thing that allows you to manually move the mower?

"13.6V with the motor off" I don't get it. WHere is the extra volt sneaking in? Been adding liquid voltage to your fuel? Unless this is really cooking the battery? 15.6 probably isn't a deal breaker, but higher than desired for continuous charging. You could charge your battery and retest seeing if it is still high. I think Kohler likes you to buy a regulator if it is over 14.8? Verify also no AC heading into the battery and no draw. You should download the manual (it's free)ENter as guest. Here is a link that might be useful: kohler