We show that the influence of spin-orbit (SO) coupling on the weak-localization effect for electrons in graphene depends on the lack or presence of z→-z symmetry in the system. While, for z→-z asymmetric SO coupling, disordered graphene should display a weak antilocalization behavior at lowest temperature, z→-z symmetric coupling leads to an effective saturation of decoherence time which can be partially lifted by an in-plane magnetic field, thus tending to restore the weak-localization effect.