Mowing LX188 loses power

[Creekpaddler]

My 13-to-16 year-old JD LX188 lawn tractor - with a 17-hp Kawasaki V-twin engine & a 48" deck - often loses power while mowing. It may run fine for an hour, but if I shut it off and try to restart the engine, it won't run. The spark plugs, engine oil, gas- & air filters are new. The service manager at the local JD dealer believes that the problem is due to insufficient fuel moving through the carburetor, and I tend to agree. Anyone have experience with this kind of problem? And the best approach to fix it?

[beenthere]

You didn't mention compression test. Or re-build of carburetor (including cleaning).
Any history of old gas left in the carb?

[Creekpaddler]

I haven't done a compression test yet. I doubt that the carburetor has been rebuilt, since I bought it 3-5 years old from the original owner and haven't touched the carb since. There is a history of old gas left in the carburetor: guilty.