I have a 1987 Grasshopper 1212 with a 44" deck and 12HP Kohler engine. It will shut off after 15-20 minutes of mowing and I let it sit for about a half hour and it just continues to repeat the cycle. I got it from a family member who had let it sit for the last 2 years but used it every week for the 2 years previous. He rebuilt the engine when he bought it. I took it to a local grasshopper dealer and they replaced belts, chains, blades, air filter, oil & filter, and greased it all up. Before I sink anymore money into it, I want to first see if anyone has any advice. I think it could be overheating, causing the cylinder to expand. I know that if that is the case then the motor will eventually cease. I know how hot mower engines can get but this one seems to get extremely hot. I replaced the spark plug because the old one looked a little foul. I had all this work done to it before I started using it so the dealer did not know about this problem.
Remove blower housing, cover over flywheel, a shop vac works great after loosening all the dirt from everywhere with a cheap paintbrush & a piece of coat hanger wire for tight spots like cooling fins on heads, be patient & take your time try to remove all debris. Most important: never use water to clean engine, will most definitely cause electrical problems.
Apart from missing air ducts the only other major overheating problem is too lean burn and that can be either clogged fuel supply or an air leak between the main jet and the inlet valve.
Using a trigger pack, check for leaks by spraying around the inlet and back of the carb with something like WD 40 which will cause lots of black smoke if it gets sucked into the engine.
Old sump oil or better still ATF will give you easy to see white smoke.
Other than that it is checking the fuel supply all the way from the fuel tank to the main jet.