Tested the generator just now, to see if I could replicate the problem Turned off the line power and generator fired up, and the automatic transfer switch transferred fine. So I put a load on the generator - electric stove with all 4 burners and oven on, and the electric dryer. No problem, but after about 10 minutes or so, the power went off but the generator stayed on. Have to go out to the generator and toggle the (70 amp) breaker to see if that was the problem. Maybe I used too much power and simply tripped the breaker (maybe when the fridge went on or something.)
... went outside and sure enough, the breaker was tripped. Toggled it off and then on again, and power to the house came on. Ran the dryer for a little while, no problem. So, I guess a stove with all burners and the oven on and the dryer is too much.