I hear the example of a theoretical rocket's acceleration slowing due to a mass gain at high fractions ofcall the time, but I think I'm missing something. If a rocket (with its propellant) is moving at such speeds that a significant mass gain would occur, wouldn't it accelerate at the same rate because the propellant has also gained mass in proportion to the rest of the rocket?

I may be interpreting the example wrong, or maybe I'm just mixed up, but this has been bugging me and any help would be much appreciated, thanks.