Several researchers have challenged the validity of this claim and concluded that the people making it are using the wrong measures of inflation and the wrong measure of worker compensation.
1) Worker compensation
Wages are just one part of worker compensation. Other forms of worker compensation include fringe benefits like healthcare. In order to see how well worker's are doing over time, economists measure TOTAL worker compensation, not just wages. There are large differences between measuring worker compensation as opposed to worker's wages (both adjusted for inflation using the CPI) as seen in the graph below.
2) Measuring inflation
Many people think that the Consumer Price Index is a good measure of inflation. It isn't, and economists agree that it tends to overstate inflation. In fact, the Personal Consumption Expenditures deflator (PCE) is a better measure of inflation of consumer goods and it is thus the preferred measure of inflation for both the Federal Reserve and the Congressional budget office. Measuring worker compensation for inflation using the PCE brings it closer in line with productivity.
However, even this is misleading. Productivity is measured using the IPD (Implicit price deflator) and thus, so should worker compensation. Comparing productivity and worker compensation while using different price indexes for both yields an inaccurate relationship between the two. As Economist Don Boudreaux has stated:
"Different inflation adjustments give conflicting estimates of just how much the dollar's purchasing power has fallen. So to accurately compare the real (that is, inflation-adjusted) value of output to the real value of worker pay requires that these values both be calculated using the same price index."
When this is done, it can be seen that worker compensation has risen steadily with productivity (with a small decoupling beginning in the early 2000s which can be explained further).
Studies on this subject:
 From the National Bureau of economics research: http://www.nber.org/digest/oct08/w13953.html
 Centre for economic performance: http://cep.lse.ac.uk/pubs/download/dp1246.pdf
 Article by Don Boudreaux: http://online.wsj.com/news/articles/SB10001424052702304026804579411300931262562
Source for graph: http://www.heritage.org/research/reports/2013/07/productivity-and-compensation-growing-together#_ftn2