We study with a 1D particle-in-cell (PIC) simulation the evolution of a subcritical perpendicular fast magnetosonic shock. The shock propagates at 1.5 times the fast magnetosonic speed. Some upstream protons are reflected by the shock's electric potential. They form a beam which carries less energy than those that are reflected magnetically by super-critical shocks. The beam triggers the growth of a fast magnetosonic solitary wave upstream of the shock, which reflects the beam protons back to the shock. Extracting the momentum and energy of this beam allows the solitary wave to grow into a proto-shock that is trailed by a short downstream region. Protons from the shock-reflected proton beam increase the density of the plasma between the shock and the proto-shock reducing its potential difference relative to both surrounding structures. Bulk protons, which cross the proto-shock, react to the decreased potential jump. The plasma behind the proto-shock accelerates and so does the shock. The trailing end of the proto-shock speeds up in order to continue reflecting the beam protons and eventually it catches up with its front; the proto-shock collapses and the self-reformation fails. A more energetic proton beam could decrease the potential jump across the shock, let it collapse and replace it with the proto-shock.