We study the stability of topologically protected zero-energy flat bands at the surface of nodal noncentrosymmetric superconductors, accounting for the alteration of the gap near the surface. Within a self-consistent mean-field theory, we show that the flat bands survive in a broad temperature range below the bulk transition temperature. There is a second transition at a lower temperature, however, below which the system spontaneously breaks time-reversal symmetry. The surface bands are shifted away from zero energy and become weakly dispersive. Simultaneously, a spin polarization and an equilibrium charge current develop in the surface region.