Many people have cited different things to either prove that it is melting, or to prove that it is not melting.

4 Ice Zones

I would classify the Antarctic ice into 4 different zones.

Seasonal Ice

Naturally, in the southern winter, the sea round Antarctica will freeze, and in the summer it will melt.  The actual area that freezes will vary from year to year, and general trends are difficult to identify.

Closer to the continent there is Ice that does not melt each year.  This ice is being pushed away from the land by the ice flowing off the continent.

Grounded Ice Shelves

Then there are the grounded ice shelves.  By far the biggest is the Western Ice shelf.  Western Antarctica is not a continent, but is an archipelago.  If there was no ice, it would be islands.

Between and covering these islands there is ice. Between the islands the ice is resting on the sea bed.  That is, the ice is not floating.

East Antarctica

The Ice sheet of East Antarctica is probably the most stable ice in the world.  It is solidly grounded on land, and is 4 kilometres thick in places.  It is slowly building up with the quite low snow falls, and is also flowing slowly to the sea.

NASA

The American National Aeronautic and Space Administration can measure the amount of ice in Antarctica by satellite measurements of the gravity.  Unlike looking at specific areas of surface ice, this method gives an overall view. 

These measurements have been done since 2002.  In the 7 years to 2009, there has been a strong trend.  The ice is disappearing.  The average reduction of ice has been about 150 cubic Kilometres a year (36 cubic miles).  A cubic Kilometer is an enormous amount of ice. The total amount of ice in Antarctica is 30 million cubic Kilometres.  So if the average rate of decline continues, all the ice in Antarctica will be gone in 200,000 years.  This is a long time.

However, the graph of the decline in amount of ice is not linear.  The rate is accelerating.  The measurements have not been done for long enough to make meaningful predictions.

One thing we can reasonably guess is that the melting of the ice will not be a simple extrapolation of what has happened for the last 7 years.

The Arctic ice and the Greenland ice cap appear to be melting much faster than the Antarctic ice.  This means that there is a smaller area of ice to reflect the sun in the north.  This is causing a strong positive feedback, and the Arctic regions are warming up rapidly.  If this happens in the south, the ice could melt much faster than it is doing.

Sources

http://www.nasa.gov/topics/earth/features/20100108_Is_Antarctica_Melting.html