for sure not the battery dropping volts that has been checked as well as fuel pressure. and by no means am I working this atv this mower is 150lbs wet and I am pulling it on flat ground there is no work involved as I could do it by hand if I had to. any other suggestions?
Running that slow for extended periods of time IS work no matter if pulling weight or not. There is very little air flow to remove heat from under the tank and under the plastics and the cooling fan blows even more heat under there when its on. I'd about bet the fuel is getting so hot its boiling in the tank. It may also be overheating the pump which will kill it very shortly too. Either way the pump will loose prime and/or stop pumping intermittently. It can't pump bubbles! lol And, as you described, it'll keep getting worse as it gets hotter until you let it cool a while or pour cool fuel in the tank.
Next time it does that remove the fuel cap VERY CAREFULLY as it can erupt like a volcano if its much full and look down in the tank. You may need a flashlight. You'll probably see the fuel boiling like a tea kettle.
If you're going to WORK your machine that way, you'll probably have to address fuel tank and fuel line excessive heat issues.
1) Using higher octane non-alcohol fuel will help.
2) Pull the tank off and cover the entire bottom with heat shield matting. Also wrap the fuel line going to the throttle body.
3) Looks like that machine already has extensive heat shields on the header and pipe just for that very reason. But you might want to remove them to also wrap the exhaust pipe with header wrap and then reinstall the shields.
All these things won't totally stop the excess heat buildup caused by running so slow over an extended time but it will help alleviate the resulting problems you're having.