userLTK has explained that not all of the ice in the Antarctic stays frozen all the time. But perhaps there's a more basic view needed : sunlight in temperate areas melts all of the ice quite quickly, so why doesn't the same happen in Antarctica?
There are a number of reasons, but the simplest (and probably most important?) is one of geometry, and the way that sunlight reaches parts of the planet's surface.
Imagine that you are shining a torch onto a ball, where the beam from the torch is circular and much smaller than the ball.
- If the beam hits the middle of the ball, it appears as a small circle on the ball's surface.
- If the beam hits near the top or the bottom of the ball, it covers a larger area of the ball's surface - so that any given point receives less light.
The same is true for the earth. Near the poles, the light from the sun is "skimming" the planet rather than hitting at right angles, and so any given amount of energy leaving the sun is spread over a wider area near the poles, and is thus less intense. So, the amount of energy landing in Antarctica per square metre is much less than it is near the equator.