Recently it was demonstrated theoretically and experimentally, that the presence of a moving conductor can break the reciprocity in the interactions between magnetic dipoles. In this article we investigate the influence of non-reciprocity on the dynamics of a pair of rigid XY dipoles, which have been realized in experiments.In particular, we focus on the energy non-conservation, which is a consequence of the non-reciprocity. We find that the dynamics indeed has regimes, wherein the kinetic energy grows quadratically. However, whether energy absorption occurs, depends strongly on the initial conditions on the dipoles. Simulations for various initial conditions reveal an intricate dependence, resulting in a rich structure of the energy absorbing regime in the initial condition space. Nevertheless, we provide a qualitative explanation of these observations, interpreting the absence of energy absorption as a confinement of the dynamics in phase space.