(quoted from post at 12:18:02 05/16/16) dc, if the battery has enough capacity to START the engine, if you're not using lights etc., it should run for HOURSSSSSSS EVEN IF NOT CHARGING WHATSOEVER (coil only draws 4 amps) so I don't see it dying shortly thereafter as caused by non charging.
If its hard to crank after its warmed up, that could be a carboned or loose or resistive cable or ground or connection or a starter motor problem and NOT the battery. After it dies and is hard to crank, will it start okay once it cools down??????????? ORRRRRRRRRR is it necessary to charge the battery before it cranks good?????????????? I would remove, clean and wire brush shiny, then re attach each and every battery and starter and solenoid or switch and ground connection and see if that helps.
Take the battery and have a shop do a free LOAD TEST.
If you want to test the charging system use my Charging Troubleshooting Procedure linked below for a complete and thorough test. Be sure the genny is polarized correct, belt is good n tight, and VR has a good ground.
Try the above and check and clean connections and run my troubleshooting then post back what you find or questions
John T
John Ts Troubleshooting