Three other possibilities, if the fuel pump isn't the issue:
On both my old Mustang and my even older Cub Cadet, the ignition coil would flake out when hot. Some hairline crack in the internal wiring would open up when warm, and then shrink back closed when cold. Very frustrating problem to find, as both would randomly die while in use, and then a little later fire right back up and run fine.
The Kawasaki V-twin on my Deere Ztrak 757 has a habit of boiling fuel in the carb bowl, when shut down after a long mowing session. After refueling and firing it back up, it runs rough for that first half minute, until enough fresh (cool) fuel is swept thru the carb float bowl to get it below the boiling point.
I've had many other small engines, nearly all 2-stroke, with clogged fuel tank vents cause a failure to restart when hot. Always easy to debug by just loosening and retightening the fuel cap, to balance pressure in the tank.
