It does sound like fuel starvation. If your genny is gasoline fueled, it could be that the gas tank is not venting. Try running the genny with the gas cap loose or removed. If that solves the problem, then replace the gas cap. If the problem still occurs, your might try changing the fuel filter.
Good luck.
2015 GMC Sierra SLT 3500 CC Long Bed
2012 Voltage 3200
2006 KLR 650