We theoretically estimate the loss rate of buried ice from spherical bodies 2-3.3 AU from the Sun. The loss rate is explored as a function of about a dozen parameters. We introduce the concept of a "buried snow line," where the loss of ice is sufficiently slow over the age of the solar system. For a dusty surface layer, ice can persist within the top few meters of the surface over billions of years, if the mean surface temperature is less than about 145 K. Variations in surface layer properties within a plausible range are unlikely to change this threshold temperature by more than 10 K. Longevity of ice in the shallow subsurface of asteroid 7968 Elst-Pizarro is plausible. Parameter regions for ice to survive over the age of the solar system exist for all of the main asteroid belt, but preferentially for large distances from the Sun and slowly rotating bodies with surfaces consisting of small particles, leading to low thermal conductivity and short molecular free paths. Rocky surfaces, in contrast to dusty surfaces, are rarely able to retain ice in the shallow subsurface.