Fuel John Deere STX30 engine cutting out

Firstly, thank you for allowing me to join this forum. My John Deere STX 30, I have owned it since new, must be nearly 30 years. It starts first time but after running ( mowing ) for about 15 minutes, splutters to a halt. After about 15 minutes I can start it again, no problem, then it cuts out again. I suspect fuel, where do I start ? It has plenty of fresh petrol in the tank.

Check to make sure the fuel cap is venting properly and not creating a vacuum in the tank. After that you may want to make sure you are not loosing spark to the plug. Can either remove and ground to engine and crank to check for spark, or those inline neon blink testers are cheap and you can install it before starting to mower , and what to see if it stops blinking as the engine is dying.