Shocks are regularly observed in the lower solar atmosphere, for example, umbral flashes which have average lifetimes of roughly a minute. For ideal magnetohydrodynamic (MHD) theory, slow-mode shocks should become unstable to the corrugation instability, triggered by the inhomogeneities in the solar atmosphere. However, the lower solar atmosphere is partially ionised, and the presence of a neutral species can stabilise the shock front. Here I present numerical results to investigate the stability conditions for a partially-ionised slow-mode shock with regards to the corrugation instability. Our results indicate that a stability range can be determined based on physical parameters of the system, where partially-ionised shocks are stable depending on the perturbation wavelength relative to the finite shock width. We relate these results to umbral flashes by estimating the wavelengths that could result in a stable shock front, and the observational consequences in terms of observing two-fluid effects in the lower solar atmosphere with the latest instruments.