It is my understanding that what drives a GAC is the available heat in the water vs. the cold in the ice. This explanation is less than scientific and my apologies for that.
So if the limit is not the availability of heat in the water, then is it the presence of ice on the surface?
Will the cyclone persist until the ice is gone? Or will it run out of heat in the water first? What is limiting?
The GAC is a different kind of heat engine, as it's a cold core cyclone. It's not dependent on the ice, as that's not what's driving the "cold end" of the engine. That's supplied by heat exiting through the top of the atmosphere.
The "Hot" side is the ocean, but I expect (and from what I've seen following various weather tools like climate reanalyzer) that heat is mostly coming in from peripheral seas, rather than from the areas under the cyclone proper. The 8C+ anomalies in the Barents figure highly here, and if you follow the storm tracks, you can see how that heat is getting fed into the Arctic proper. The storms run up the eastern seaboard of N. America, through the GIUK gap, and hook into the Barents. From there the flow has tended to pick up more energy crossing north from Europe, passing over the Kara and then swinging over Severnaya Zemlya into the Laptev after which it gets picked up in the orbit of existing high latitude lows.
At least, that seems to fit what I've seen.
