Power loss after warm up

May need to let warm up longer. You usually turn the choke on to start. You then need to turn it off to accelerate. If choke is automatic it needs to be cleaned/adjusted. It would also help to add a fuel system cleaner to your fuel.

Sounds like the choke is stuck part closed, check the cable and choke arm function.

choke is only to be used when there is difficulty in starting the vehicle generally in cold condition. immediately after the engine starts the choke should should be pushed to off AND NEVER TO BE USED WHILE DRIVING.
Also battery has nothing to do with power loss while driving or idling. I would advise calliberation of the carburetor & if problem still persists to get the timing checked.

Start procedure is, push the primer as many times as it takes to 3/4 fill the bulb ( you cannot over prime it ) pull the blue choke lever fully out,place the saw on the ground with your right boot through the back handle, crank the engine until it fires once, do not continue to crank the engine with the choke out ( they will not run on choke, only fire ) push the choke fully home, crank the engine until it starts, blip the throttle trigger to bring the saw to idle, warm engine, pull the choke fully out and push in again without cranking engine, this will engage the part throttle, crank the engine until it starts, blip the throttle to bring the engine to idle.

this sounds like a fuel problem , clean the carbs, but replace the plugs,airfilter and oil at the same time

Most Generac generators have a lever for the choke that pulls out. So if the generator is being started for the first use or cold you should choke when starting . Let it run for 30-45 sec. then push it in . Once the engine has been run or warm you dont need to choke every time when starting .

One thing I noticed right away is you say full choke for 6 miles, WOW, that might be your cause, one of the spark plugs is gas-fouled. Change out the plugs, let the bike warm up some before you drive it so you don't have to use the choke/enrichener knob as much as you do. Let me know how that works out. BTW, I warm up my carburated HD until no choke is needed before I ride away, it can and does take some time.

you need to take your carb off give it as good cleaning. also check your intake gaskets where the manifold joins the jugs and the black rubber one where the carb joins the manifold. You def have air/fuel problem going on. also check your vscume hose to the carb but im thinking that is not it.

auto choke staing on check operation