In this work we estimate the minimum persistence time of subsurface ice in water rich sediment layers remaining after sublimation of a martian lake. We simulate sublimation of ice from layers of different granulations and thicknesses. Presented results assume insolation and atmospheric conditions characteristic for the present day southern Elysium, where data from Mars Express have identified surface features possibly indicating the very recent presence of a frozen body of water [Murray et al., 2005. Nature 434, 352–356]. The age of these features is estimated to be several million years. On this time scale, we find that most of the water ice must have sublimated away, however remnant ice at a few percent level cannot be excluded. This amount of water ice is sufficient for chemical cementation of the observed features and explains their relatively pristine appearance, without significant signs of erosion.