We report non-equilibrium magnetodynamics in the Rashba-superconductor GeTe, which lacks inversion symmetry in the bulk. We find that at low temperature the system exhibits a non-equilibrium state, which decays on time scales that exceed conventional electronic scattering times by many orders of magnitude. This reveals a non-equilibrium magnetoresponse that is asymmetric under magnetic field reversal and, strikingly, induces a non-equilibrium superconducting state distinct from the equilibrium one. We develop a model of a Rashba system where non-equilibrium configurations relax on a finite timescale which captures the qualitative features of the data. We also obtain evidence for the slow dynamics in another non-superconducting Rashba system. Our work provides novel insights into the dynamics of non-centrosymmetric superconductors and Rashba systems in general.