Frank, heres the bottom line..Power flows from your ignition switch through your PTO, neutral and clutch safety switches.
To the starter solenoid (black/white wire??) When all the switches and battery etc. are new there is very little resistance.
After you get some time and some age in these components resistance builds up and eventually will cause a voltage drop by the time it gets to the starter solenoid. This voltage drop will vary according to temperature, humidity and other factors.
That's why some times it'll work and other times it wont. The starter solenoid needs approx. 9 volts to fully engage. Anything less and it wont fully make contact to send power to run the starter motor. Yes it will click, but needs just a little more "oomph" to fully seat on the contacts and allow the starter motor portion to run. Now instead of replacing all the components in the system to reduce the voltage drop. What you need to do is install a starter relay. Most, if not all modern machines have this feature now because of this very problem. Some companies figured this out a bit sooner than others and came up with a pre-wired relay kit with instructions (John Deere and Scag I know for sure). Now some guys like to do things on there own and run down to NAPA and get a regular low voltage relay or a good old fashion starter solenoid, wire it up themselves and fix this problem, which works just fine. However the good old fashion starter solenoids still need close to 9 volts to engage and still causes some problems. The low voltage relay is the best way to go.. I think it will work with as low as 4 volts. In my experience the easiest way to go, is to install the JD kit part #
AM107421. It's, like I said, prewired and comes with instructions and it's around 15-20 bucks. Basically the way it works is... The red wire goes to the Battery terminal of the starter, the black wire goes to ground. You plug the black/white lead that would normally go to your starter to the male purple connector of the relay and the female connector purple lead to the starter. I have solved this "mysterious" problem many, many times on all brands and models of older machines with this kit. Everyone has given great suggestions for making sure your basic electrical system is sound and in proper working order. Most times when all else checks out and I have verified that voltage to the starter solenoid is a little low or questionable, installing this kit solves the problem at least 99% of the time. I'd be willing to bet it will work in your case as well. On rare occasions I have torn down the starter to find the contacts bad in the solenoid when this kit would not solve the problem. However for the price of the kit it's more than worth a shot in my opinion..................