smokey-truck,
Is your gen running through the original relay box, or does it have a later model regulator fitted?
Because if this has been done, it will quit when you remove the battery cable.
But none of this should matter as long as the thing is charging properly to start with.
Now you know the generator has been tested and is up to scratch.........look at your voltage regulator and make sure it is functioning properly and getting all that power fed back to your battery.