Yes, the engine should run a great number of hours if properly maintained, however, there is a lot more to a ZTR than just the engine, and those parts do wear, and can and do create their own issues. As an old farmer once told me, being a farmer isn't enough, you need to be well versed in veterinary care, and be a good mechanic to keep all the farm machinery working the way it was designed to be. If you don't have the skills that are necessary to repair your own equipment, then you are doomed to pay someone else that does. I would suggest that you purchase a factory shop manual for your particular machine, and start reading it. Sometimes you will need to read it a few times just to digest what is on the printed page, and there is nothing to be ashamed of when you do that. I was a mechanic in my younger days, and technology overtook my skills. I can still work on things that are mechanical, but when it comes to complicated electronics, I am at a loss and have to defer to the younger generation that understands the principles of modern technology. If I owned your machine, I would start by looking for any wear in any of the functions that move, such as the handles. If there is slop in those, you have to eliminate that slop before you can make the adjustments to the switches.
I own a Corvair with a 4-speed transmission, and the shifter developed problems. Being that I understand how the shifter transmits the motion to the transmission, I was able to find the root cause of the problem. It was both a pin that had developed wear in it and the fact that the hole that the pin goes through had also worn. It now shifts as it did back in 1964 because I remove all the wear that it had accumulated over 50+ years. Knowing where to look is half the battle to get any machine back to its "like new" performance.