Update 3 years later.
Thought I would update this thread again since the problem occurred again 2 months ago, 3 years after the original problem, in case there are any other 344H owners having the same problem. This time I went through 2 ignition relays and finally had enough and called in the Tech from my Deere dealer. He was great. He spent the time to really trace out what the problem was. He came up with a TSB about the possibility that the wiring in the Red Dot A/C unit upgrades that Deere was offering may be wrong. I had suspected that the load this A/C unit put on the electrical system was part of my problem 3 years ago and I had disconnected all that wiring back then and I wired the A/C unit direct to the battery's bypassing the machines electrical system so he said that I had taken care of that problem back 3 years ago. This TSB did key the tech on to what the potential problem might be. The TSB was about a problem with an aftermarket A/C unit and he took notice that this machine had an aftermarket Two Way radio installed in it. What he found was a combination of a loose terminal at the ignition relay caused most probably by excessive heat becuase of the improper installation of a two way radio, installed by a local radio guy that had tapped into one of the ignition wires. Between the loose connection and the fact that the Deere tech found that when the two way radio was just scanning it drew .3 amps but when you key the two way to transmit it draws 12 amps. This explained why the relays were heating up and failing. The diagnostic was to turn on all the lights, AM/FM Radio, Heat and then take amp readings at different spots according to the schematic. He found that with all this stuff on, as soon as the radio was keyed to transmit, it was jumping the amperage up over the rated 70 amps of the ignition relay. The two way was disconected and he replaced everything that had taken heat and the machine seems to be good as new. I went back over in my head when the last time the machine died before I called the tech in and it was when one of my operators was plowing snow in one of the college parking lots and the machine had all the lights on, heat, am fm radio, and he said he remembered picking up the two way to call public safety for something and the machine just died. Guess this splains why!
I know but i had to say it just sounded like it just ran out.Check any realys if there are any that can be switched from one to another because i had kinda a similar problem with my case , in that it would not go forward or reverse and it happended just like that. we checked realyays that we could and the odd sized ones that felt fine and so forth were not.