Excellent call Farmer Tom. Good place to start. Doesn't cost anything to loosen the gas cap. I've seen the vent tube on the top of the tank and never thought where it actually vented the tank (and still haven't checked since the tractor is over at my son's house).
Had a Harley I had a hard time keeping running. Would start fine, run for a while then die. Let it cool down, start, run, die. Checked the coil and it was cracked and very hot. I suspect the previous owner didn't change out the coil when he upgraded to the electronic ignition (different ohm rating). Changed out the coil and it would run fine
Finally got the bike road worthy and took it for a spin. Cruising down the highway it started loosing power and died. First thing I checked was the gas level. It was all fine. Restarted just fine and motored on thinking it was just a hiccup. A few miles later same scenario. I then figured out the vented cap was clogged. Replaced cap and all was well.
Same thing started happening again after awhile. Run for an while die, wait, start without a problem, repeat. Checked coil. OK Checked cap OK
Scratched head a lot, read a lot, scratched head some more, left it in the back of the garage for a while then read somewhere the old circuit breakers would get hot and trip. Replaced the circuit breakers and that seems to have solved the problem. Now I just have to clean out the carb again since I let it sit too long. Then I can really check it out.
Same MO each time, different problem. Which frustrated the hound out of me, BTW.
Sometimes it is a simple find and fix, sometimes it is a combination of things (or one things leads to another). That's why forums like this are so helpful. The collective knowledge base can really help folks out.
Edit to add: The 1010 vents off the filler neck through the long tube on top of the tank. You cap may be fine but the tube may be clogged. Give it a puff of air and see if it is clear. You'll probably have to take off the hood to get to the tube.