Got the new solenoid under warranty, installed it and the tractor seems to be running fine now. Cleared about an acre with the bush hog and no problems with the engine cutting out. Getting the thing installed was a real pain in the posterior though. The threaded hole it goes into does not have tapered threads but is flush with the surface of the block. That, along with the tight space, makes it hard to get the solenoid positioned properly to get the threads started. Even getting the plugs connected together with my fat fingers was hard due to the wiring harness being just long enough to allow them to connect. Even another inch would have made plugging them back together much easier, especially when slick with dielectric grease. And I was lucky I was able to start the tractor and raise the loader before I removed the bad one. I hate to think of putting the cursed thing on with the loader arms down and in the way. Anyhow, everything seems good now. Thanks for everyone's assistance in helping me solve my problem.