The engine, in good standing, is good for 4KW+. If the generator head had issues such as a shorted winding, poor brushes or failing field, it just wouldn't create a 4KW load on the engine.
I almost hate to suggest this because I know someone is going to slap me for this but, to rule out fuel related issues, you can get a can of ether starter fluid such as below and when the engine starts to bog down, spray just the smallest mist you can create into the carb. If the engine 'wakes up' for a few seconds you know the problem is fuel related. I can't emphasize enough to be careful not to spray too much ether. While using ether, YOU become the carburetor. If it starts to run away, hit the kill switch.
