I use an E3 spark plug and Mobil 1 Extendend Performance oil in our 11 year old built-in Onan generator. During storage in our back yard I exercise it for 30 to 45 minutes each month powering a 1500 watt portable heater. For the monthly exercise sessions I run it 1 minute before turning ON the heater and run it for 1 minute after turning OFF the heater.
We run it for short or long runs when camping and it always starts right up. It's very quiet and smooth running for a 4KW generator, as Winnebago installed it fairly well isolated. I believe the E3 spark plug also has something to do with it's low-vibration smoothness and unlabored humming sound, as it sounded and felt different using stock spark plugs. It's also supposed to be a bit less polluting and use less fuel.
As far as I can recall, the operator manual doesn't mention anything about short runs harming it, although common sense tells me it might wear out the starting mechanism faster.
By the way, does anyone know what Onan RV generators didn't use a starter? They supposedly were started by the starter button applying battery DC voltage to a section in the generator coils such that they acted like a "motor" to spin the engine and start it? On the surface this sounds like brilliant engineering - no separate starter motor or gears to wear out.