A rocket using chemical energy at a constant rate does not have this problem, because the excess energy it seems to gain from kinetic energy going up quadratically is balanced by a decrease in the kinetic energy that the expelled reaction mass is left with.
If you think of mass as the deformation of spacetime, mass reaction engines push off the wake from expelling mass rapidly in one direction to go in the other direction.
The EM Drive is an energy reaction engine, rather than a mass reaction engine (if it works as described), so instead of pushing off wake, it uses energy itself to "deepen the fold", as it were, and increase speed (and mass, since the two are exchanged).
That's interesting. I've never considered that the very act of increasing the velocity of the EM Drive would actually increase its mass. Hrm.
Not disagreeing with you there, but I don't see how that leads to free energy from an emdrive. How exactly do you get more energy out than you put in?
And anyway, kinetic energy isn't a conserved quantity. It can be converted into potential energy in a gravity well, or lost entirely in inelastic collisions. Momentum is the quantity that is always conserved, and that is what the emdrive violates directly (though still not in a way that allows for perpetual motion or free power, near as I can tell).
As jack9 proposed higher up in this thread, you could put the EmDrive on the outside of a rotating system to provide constant torque, which accelerates the rotation. Then wait until the system has sped up to the point where the kinetic energy increases faster than the power you put in. Then use the whole thing to drive a generator.
