Why hasn't unemployment recovered yet?

To answer that question, let's compare this recession (aka the "Great Recession") with the preceding one.

The early 2000's recession

The early 2000’s recession lasted 8 months (March 2001 - November 2001). The GDP dropped a barely noticeable 0.3%. Unemployment rose from 4.3% to 5.5%. But, like the recession before it, the unemployment rate kept on rising after the recession had officially ended, peaking at 6.3% in June 2003. The unemployment rate has never dropped back down to where it started. The closest it came was 4.4% in October 2006, one month short of five years after the recession officially ended.

The "Great Recession"

 

The "Great Recession" officially began in December 2007 and lasted eighteen months, officially ending in June 2009. That's more than twice as long as the preceding one.

This recession was by any standard much more severe than the previous one. The GDP dropped 5.1% (a huge decrease compared with the last one). The unemployment rate rose from 5% in December 2007 to 9.5% in June 2009. Like the preceding two recessions, unemployment kept on rising, peaking out at 10% in October 09. So far, it’s dropped back down to 7.8%.

H's a chart that compares the GDP growth rate for both recessions:

As you can clearly see, the Great Recession (in red) was clearly both longer and more severe in terms of GDP than was the previous recession (in blue).

Now that we've compared the recessions, let's compare the recoveries.

Comparing the recoveries

After the last recession, it took the unemployment rate almost exactly five years - after the recession officially ended - to fully recover. We haven't reached the five year mark, and won't until May 2014.
Here's a graph comparing the unemployment rates:

Unemployment following the 2001 recession (blue) and Great Recession (pink)

This downturn has been much more severe than the last one. And we won't reach the point where the recovery from the 2001 recession was complete until the summer of 2014.