If the voltage is in fact going away under load then returns right after the load is removed you have a connection that is opening up via heat, an may re-power as soon as it cools down. Common electrical issue, nothing more. It can be tracked down in many different ways depending your skill level, an metering or lack thereof, on hand.
Thank you for the suggestions.
It turns out it may have been a particular appliance that may have had a power factor of less than one as suggested by RedOctobyr
I'll be testing that same small portable heater today with standard AC from a home wall socket to see what the VA and watts are that the portable generator could not handle.
To clarify - I'm not a Predator, but one of my Generators IS
HarborFreight Predator 3500 Inverter