It is known that oscillatory domain-wall (DW) motions in soft magnetic thin-film nanostripes above the Walker critical field lead to remarkable reductions in the average DW velocities. In a much-higher-field region beyond the velocity-breakdown regime, however, the DW velocities have been found to increase in response to a further increase of the applied field. We report on the physical underlying mechanism of this unexpected behavior. We associate the mechanism with the serial dynamic processes of the nucleation of vortex-antivortex pairs inside the stripe or at its edges, the nonlinear gyrotropic motions of vortices and antivortices, and their annihilation process. Moreover, this work evidences that a two-dimensional soliton model is required for adequate interpretation and understanding of DW motions in the linear- and oscillatory-DW-motion regimes as well as in the beyond-velocity-breakdown regime.