I agree with the person who said "Generator Problem" but disagree as to the specific.. What you describe "Reving up and slowing back down, Reving up and slowing back down" is called HUNTING and it indicates a too rich fuel air mixture on a governor controlled engine. (This is what I get for being trained in small engine work) too lean causes misfire by the way. Now I'm not saying that is the only possible cause, but if you have something like a Progressive Dynamics HW-50C installed post-Transfer switch, it will lock you out when the Generator is doing that.
you need a tune up.(An old fashion one) or, perhaps, a new air filter. or (most likely) BOTH.