Engine not charging battery engine dies when battery is removed

With the engine running, connect a dvm across the battery, in high idle, your meter should read 13.5 to 13.8 VDC, indicating proper operation of the charging system, if your meter reads, battery voltage or below, it is most probably your voltage regulator, which is located on the right side of the engine, it has 3 wires connected to it, one of the wires is violet, it is easily seen, there is a raised number on the item, it is attached by one 1/4 x 20 x 1/2" bolt, easily removed, contact a kohler dealer and read the number to them, ensuring that you purchase the correct regulator.

I had same. Flywheel magneto is the charging system. Turned out the magnets under the fly wheel are glued in and all fell out. Pull the flywheel, important to mark the order of the magnets, sand and clean each magnet and inside of flywheel then epoxy them back in (JB weld worked for me). Replace it all and done. Otherwise a new flywheel and coil set will run you about $500. It's a pain getting it all apart, and you need a wheel puller to get flywheel off , but beats the alternative!

When you remove the battery it will break the circuit and die and if your battery dosen't have at least 5v in it it won't charge and you will have to replace it.