You're right about the engines not pulling down.
My 30KW Protector diesel shut down on overload once.
We had a couple day's outage, and I was working in my shop, which the genset is adjacent to.
My wife was doing some housework, and I could hear when the load changed as she turned stuff on and off, as the tone would change a bit, and I'd hear the turbo wind up, but the RPM never dropped enough to detect.
Eventually I heard it load up and stay loaded about 10 seconds, then the lights went out and it shut down.
I walked outside and it had a "Shutdown on Overload" on the display.
I had about 3KW of lights on in the shop, plus the shop A/C was running.
I went in the house and asked my wife what was the last thing she turned on before it shut down.
Well, she had both washing machines running, and at least one dryer, the heat pump was running, she had the oven on, as well as 2 surface elements, and had started to fill the sink with hot water. (I have a 27KW tankless water heater).
I suspect one of the washers was filling, and when she turned on the sink faucet, the extra flow ramped up the power on the water heater and that's what put it in overload.
I had a little talk with her, and explained that the genset could run ANYTHING in the house, but not EVERYTHING in the house. LOL
As far as Mattyman's problem, could it be the voltage regulator isn't ramping up the field current enough to maintain voltage, which would explain the rpm remaining constant but the voltage dropping.