You are still confused:
The second sentence is correct although it is repeating what I told you. The first is (apparently) wrong. The problem is that you are jumping between referring to the ship alone where the energy is not conserved and the closed system (ship + reaction mass) where the energy is conserved. It may be that that is not what you intended to say this time but in your first post you made you made the false suppositions based on the calculations of the kinetic energy of the ship alone and this looks like more of the same.The energy gained (or lost) by the ship is different in different frames of reference, but total energy is still conserved in each frame of reference.
The ship and the reaction mass forms a closed system that conserves momentum and energy.
Yes it does, as I said:The ship and the reaction mass forms a closed system that conserves momentum and energy. If the ship and the reaction mass starts accelerating away from each other the total energy of the system increases, that energy has to come from somewhere and the power required to maintain constant acceleration will increase with time. I don't see where the power comes from, if not the drives of the ship?
This is not the issue. The problem in your first post was that you ignored reaction mass and thus drew the wrong conclusion about constant power/acceleration and restrictions on acceleration.The crux of this is that we always need to consider the whole mass system not just the primary (craft) but the reaction mass as well. The reaction mass has its own, mass, velocity, momentum and kinetic energy. When we do this the invariant Power Plant energy is distributed between both the primary mass and the reaction mass (both receive equal and opposing momentum). The total change in kinetic energy of both the primary and the reaction mass equals the total propulsion (power plant) energy but the proportional distribution depends on the frame of reference.
It was I think, fairly obviously an ejected reaction mass (Fusion, HEPlaR) I was referring to here.In the frame of the ship, the reaction mass keeps accelerating away from the ship, it does not start from zero in every instant.