I am getting the impression that you are not running the engine near its maximum throttle position. You need to run the engine nearly full throttle at all times when you are mowing for a number of reasons.
Running the engine near full throttle gets the maximum output of current from the engine alternator, and you need that to ensure there is enough voltage to keep the PTO clutch engaged.
What you have described sounds very much like the battery became so weak that it could not keep the PTO clutch engaged by the time you got near the finish line of your mowing.

Always listen to mownie, and I agree with his assessment.

Charge your battery, and check the electrical connections, paying particular attention to the battery cables - both of them. Also take a look at all the wiring and connections that feed the PTO, as well as the engine ground wire. Intermittent problems frequently result from corroded connections and/or frayed wires.

Among the reasons to run at full throttle include battery-charging, as mownie mentioned, blade speed, and ensuring good oil flow. Your Kohler engine has an oil pump, but some engines are splash lubed, which makes high engine speed even more important. As a general rule, virtually all small engines should normally be operated at (or very near) full throttle.

Post back if these suggestions don't fix your problem; there are a number of possibilities.

I always keep it at full when mowing. The varying was just a random idea that popped into my head.
From the tinkering I was able to do today, it looks like the ground bolt came loose.

Found http://forums2.gardenweb.com/forums/load/tractor/msg060934286991.html to be very helpful.