The Wikipedia article on the subject of the "Antarctic ice sheet" says that:
The icing of Antarctica began in the middle Eocene about 45.5 million years ago and escalated during the Eocene–Oligocene extinction event about 34 million years ago.
The article later says that:
Ice enters the sheet through precipitation as snow. This snow is then compacted to form glacier ice which moves under gravity towards the coast.
However it looks like, from the photos of Antarctica, that this transfer of ice to the coasts is not happening everywhere on Antarctica. Rather, many places seem to be under a perpetual ancient ice cover.
If the precipitation was recycled at a continuous rate everywhere, it shouldn't be possible to obtain a 1.5 million year old core sample (according to an article in Nature) or structures such as Vostok Station that covers an ancient lake.
A similar location is Dome F that according to Wikipedia has a yearly precipitation of about 25 mm (millimeters; approx. 0.98 inches).
So the question is, if we have a 25 mm precipitation per year for even just 10 million years, we should have an ice cover that's 250 kilometers thick. Or if we had it during just a 5 million year time span, it should give us an ice cover that's 125 kilometers thick.
Reasonably we could allow for some compression of the ice but still keeping in mind that we are not talking about a neutron star here.
How come the current Antarctic ice cover is just a couple of miles thick?