tinkerer,
The QD7500 is a great generator. For the most part, seriously reliable. But, on occasion, it will hiccup. Normally if a QD is having issues, it will run but, shut down prematurely and, will present a "code" in the form of flashes of the LED light, inside the red toggle switch. It will flash a certain sequence, pause, then flash the same sequence again. And example would be:
three flashes, a pause, then, three flashes again and, a long pause, then it starts all over again.
Those three flashes represent a "3". And, the second set, also represents a "3". So, the code would be, 33. So, in cruising around in the trouble shooting manual for Onans QD7500, you'd look up the code 33 and find out what it means and, how to possibly remedy it.
Now, as for your problem. If you're not showing a code of any type on that toggle, then it's maybe possible you have either a bad connection on the ground side for the ground cable entering the back side of the gen or, even a possible bad connection on the positive side too. It's good enough to carry a lighter load, as in the fuel pump and or, even the glow plugs but, when it comes to a big load, like the starter, it may be faulting out. No guaranty on this, just a hunch. Sorry I could not be of more help. Please post when you've found the cause.
Scott