Domain-wall (DW) motion is a crucial process involved in magnetization reversal, be it under magnetic field or spin-polarized current stimulus. In most cases the DW speed does not exceed ≈100m/s and collapses above a given threshold of the stimulus, an effect known as Walker breakdown. A few specific material properties have been identified to delay the breakdown of speed by increasing the energy barrier preventing internal precession. We show that in a 3D nanomagnetic system, here with vortex-state domains, the topology of the magnetization distribution may intrinsically and robustly delay the Walker breakdown due to an exchange-spring effect. However, in contrast to situations in lower dimension, the motion remains steady-state. In addition, curvature induces a major non-reciprocal effect, delaying or not the Walker breakdown depending on the sequence of chiralities of the azimuthal domains on both sides of the DW, independent of its direction of motion.