Well...If you watched what happened from instant to instant, in each instant the observers are separating at constant velocity and at this instant A and B would see each other's masses change according to special relativity. The only thing that breaks this symmetry is that we see that Observer A is the one that has used their rockets, and we have decided that Observer B will define the unaccelerated reference frame. If B were on the Earth and A were in a rocket, it is clear that any mass change would be ascribed to the motion of A, however, B looking at A would still see A moving away at increasing speeds relative to A's rest frame, which is a perfectly 'proper' frame for them to be using. Even if B were on the Earth, A would still see B and the Earth gain mass, even though A would never try to assert that they are in fact stationary and it is B and the Earth which are mysteriously accelerating away from A.
Relativity isn't slavishly symmetric when you establish who is actually doing the accelerating.