I tried in vain to find the answer to this question on the web, but all it would tell me was, "it is very deep", and "it is known as a thaw line rather than a frost line in the arctic and antarctic". How far down you would have to live to escape the permafrost? 100 ft? 1000 ft? 10000 ft?. How feasible would an underground base be?
According to "Permafrost, active-layer dynamics and periglacial environments of continental Antarctica" South African Journal of Science 98. pages 82-90:
Only 25% of Antarctica has permafrost, as the material beneath thick ice sheets is not permafrost.
The deepest permafrost occurs where there is no ice sheet.
The deepest permafrost in the Antarctic is about 1000m.
If you have permafrost and an ice sheet begins to form on the land, it insulates the ground from the super cold air. Geological heat should then begin to melt the permafrost slowly from the bottom up. If the ice sheet persists for a long time, and is thick enough, like over East Antarctica, the permafrost should disappear until there is water at the bottom of the ice sheet. Any methane produced by rotting vegetation or venting coal, oil or shale in deeper layers should combine with this water, especially since the pressure is great at the bottom of an ice sheet, and form a layer of clathrate. Clathrates, if enough pressure exists can form up to 30 degrees C. The temperature at the bottom of a thick ice sheet should be at the melting temperature of ice which at such depths is a couple of degrees below zero.