I realize this thread is solved. However, a stuck fuel cutoff solenoid on the carburetor will also cause this problem, for any future troubleshooters. It lets just enough fuel in to start and run, but not enough to keep running.
I found this problem on one of my machines, even though I put in a lot of fuel conditioner at the end of the season. I had a spare carb laying around and the solenoid was stuck on that carb too. Easy to take off and clean the ethanol varnish out.
To diagnose, put your finger on the solenoid and turn the key on. You can feel (and usually hear) it retract from the main jet.
As of this year, I've finally thrown in the towel and only run ethanol-free gasoline. Costs about $1.50 more per gallon but I've wasted way too much time over the years with carb cleaning.