Toro zero turn mower. Kawaski engine. Battery won't charge while in use. Mower starts and run fine until battery is drained. Voltage regulator has been changed twice same problem. What charges the battery, and how do I prove it out

May be the fuse is blown. It has a charging coil under the flywheel with a wire going to the rectifier which goes to a fuse somewhere on the way to the ignition switch.
Here is one of the Kawasaki mower service manuals and may be helpful
LOL
http://www.toro.com/customercare/commercial/education/pdf/k_fe120.pdf

Hi,
You should have 13.4 - 14.6 V DC at the battery charged and nothing going on. Once running you should have 26 -36 V AC coming from the stator(under the flywheel with wire(s) going to the regulator.) You should have 14.4 - 16.6 V DC leaving the regulator and returning to the battery(can be measured at the positive battery terminal.) It is the electric PTO clutch that is draining the battery because something in the charging circuit has failed, or a wire is broken.
Peace,
Clarke