if the vent on the gas cap is plugged that too would give you the same symptoms and loosing the cap is easy and no cost to try.
I have a John Deere that every now and then, I just unscrew the gas cap a bit then screw it back down. If I don't then it will eventually die. I bought one new cap and the same thing started happening a gain. Rather than buy a second, about every hour of running I just undo it a little then tighten, no problems. I think Deere must have hired some Microsoft engineers, you know, "It's a feature, not a bug".