It could be that there is poor flow of fuel to the carb itself. It runs itself out of fuel in the bowl and dies. I would check that the fuel shut off is open and good flow first. Fuel pump on these? Try it w/ the fuel cap loose to ensure it is venting. A can of carb spray would be useful. If you go this far and still not running, a squirt down the throat of the carb as it is dying would tell you if you still have spark anyways and would indicate you need to go further w/ the fuel system. There could be other issues pertaining to ignition as well. Let us know what you learn.

I have totally cleaned the carb., bowl was little trashy. replaced all fuel line, fuel shut off is working as it should, cleaned the fuel tank, lots of trash in it. I am replacing the air filter and spark plug this week. I also replaced the ignition relay, that turned out to not be the problem. It has to be in the fuel system. No fuel pump on this one. from tank to carb. i will let you know hot it turns out tomplum, thank you very much for your assistance.

i dont know where to find the engine model number on my rx75 motor. i just think it does not have one

It will be a decal on item #1- the top engine shroud. Looks like it could be one of the Fc290v series. Are you having dificulty looking up parts?

Here is a link that might be useful: Deere parts