I have a newer propane-fueled Onan generator. It experienced a similar problem to yours a few months ago. Turns out the voltage regulator had died.
Mine would crank and crank and crank, but never actually start. While it's cranking the spark plug gets electricity from the house batteries. But as soon as it starts, the spark plug quits drawing from the batteries and draws from the voltage regulator instead. Since the voltage regulator was sitting there doing nothing, on the very first ignition stroke after starting, there would be no ignition and the engine would die. Which of course made it seem as though it had never started at all.
When I took it to my local Cummins/Onan dealer, they pulled the voltage regulator and showed it to me. It was quite literally scorched. Once they popped in a new regulator, it ran like a charm.
I thought getting old would take longer!