By using the self-consistent Born approximation, we investigate disorder effect induced by shortrange impurities on the band-gap of a seminal two-dimensional (2D) system, whose phase diagram contains trivial, single-band-inverted and double-band-inverted states. Following the density-ofstates (DOS) evolution, we demonstrate multiple closings and openings of the band-gap with the increase of the disorder strength. Calculations of the spectral function describing the quasiparticles at the Γ point of the Brillouin zone evidence that the observed band-gap behavior is unambiguously caused by the topological phase transitions due to the mutual inversions between the first and second electron-like and hole-like subbands. We also find that an increase in the disorder strength in the double-inverted state always leads to the band-gap closing due to the overlap of the tails of DOS from conduction and valence subbands.