Start by having the generator professionally load-tested. If one of the six internal diodes is defective you will loose exactly two thirds of its rated output, and that isn't enough to run the entire electrical system, particularly at low engine speeds. It's not common but a diode can be intermittent so any testing has to be done while the problem is occurring or at least under the same conditions. With a bad diode, "ripple" will also be very high. That is displayed as a voltage on some testers and a relative bar graph on others.

The typical generator is designed to deliver around 90 amps. With a bad diode you will only get about 30 amps.