Apologies ...
As an example ...
Activated the engine, and the button disappeared. Used the drive to warp to a distant moon, after arriving in the moons sphere of influence, set throttle to zero and shut down warp engine, but the Auto-circularize button did not re-appear. (should it?) ... switched to a distant target and switched back to the ship, the button is there again and Auto-circularize works as normal. ... does this help?