Have you been doing the scheduled maintenance? I had my genny starting to shut down on me occasionally about 2 months ago. On this last trip over the 4th, it started happening more and more frequently. It got to the point where it wouldn't even stay on for more than a couple of minutes.
Out of ignorance, I hadn't even looked at that thing the entire year that I've had it. Most of my RV'ing friends hardly ever use theirs, so the conversation of maintenance never came up--because they didn't know. Turns out in my case, putting 215 hours on that thing without even checking oil isn't a good thing.
Either that, or not having any oil left in it a and it having it keep on shutting down is pure coincidence.