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My name is XXXXX XXXXX I am going to assist you with this.
First, I must explain a little bit about how your genset operates, to help you understand what is going on here.
A genset is composed of 2 major components - an engine and a generator, commonly referred to as an alternator. hf
A generator is composed of 2 major components - a rotor, commonly referred to as an armature, and a stator. The stator typically has 2 or more windings - 1 or more power windings, and a smaller exciter winding.
There are 3 things required for the production of electricity - a magnetic field, a conductor (wire), and movement between the field and conductor. Since the field has no physical mass, it is much easier to move it than to move the conductor. We move the field by spinning it with the engine. This is why most gensets are known as revolving field gensets.hf
When you start the engine, the rotor starts spinning (it is connected directly to the crankshaft of the engine). When stopped, the rotor retains a tiny amount of magnetism, called residual magnetism. This RM acts as a 'jump start' for the electricity making process. It creates a tiny amount of electricity in the stator, which is sent to the voltage regulator, converted to DC, and is sent back to the rotor via the brushes and slip rings. This increases the amount of electricity being produced in the stator, until 120V is reached.
This turns the rotor into an electromagnet. As it spins, the magnetic field around the rotor is passed through the windings of the stator (conductor). The magnetic field aligns the electrons in the wire and makes them move. This flow of electrons is electricity.
Remember, a magnet has 2 poles - north and south, or positive and negative. As the positive pole passes the windings, it moves the electrons in one direction (the positive pulse). As the negative pole passes by, it moves the electrons in the opposite direction (the negative pulse). One positive pulse and one negative pulse are one cycle, or Hertz. Since US power is 60 Hz, this process must happen 60 times per second (50 times per second (50 Hz) in much of the world).hf
We now have nominal voltage flowing (120 V in the US).
When a load is applied to the genset, this voltage drops correspondingly to the size of the load.
The voltage regulator senses this power drop from the exciter winding and says ‘Hey, I've got a load on and the power is dropping. I'd better make more power'. It does this by increasing the DC voltage to the rotor, which creates a stronger magnetic field, which pushes even more electrons into movement.
The VR constantly monitors this voltage and adjusts the field accordingly.
We now have electricity.hf
What is happening with your set, is that the rotor is not able to maintain this residual magnetism - it is dissipating.
By charging a small amount of DC voltage back into the stator, you are doing a procedure known as 'flashing the field'. The field is the windings in the rotor, and flashing it restores a small amount of the RM, which allows the set to start working.
Unfortunately, the only way to cure this is to replace the rotor. I checked with the sources I have available, and through them the rotor is no longer available. You would need to contact a Honda dealer to see if it is still available from Honda. I have no idea what the cost would be, but suspect it would probably be cheaper to find another genset.
If you would like to do some digging to see if some obscure shop somewhere may have a rotor, the part number is XXXXX
Otherwise, you will have to resort to flashing the field when you need to use the genset.