In order to get an accurate picture you have to look at compensation and not just wages. Compensation is wages+benefits, and benefits are becoming an increasing portion of compensation. The ACA has mandated healthcare benefits be provided for many workers, so the trend isn't likely to go the other way anytime soon I imagine. It's a losing proposition for an employer to spend more (in terms of wages, benefits, and other costs) on a worker than the workers adds in value. I don't deny wages haven't increased as much as productivity, but wages are only part of what people get for working.
The NBER article I cited earlier states the issues:
Two principal measurement mistakes have led some analysts to conclude that the rise in labor income has not kept up with the growth in productivity. The first of these is a focus on wages rather than total compensation. Because of the rise in fringe benefits and other noncash payments, wages have not risen as rapidly as total compensation. It is important therefore to compare the productivity rise with the increase of total compensation rather than with the increase of the narrower measure of just wages and salaries.
The second measurement problem is the way in which nominal output and nominal compensation are converted to real values before making the comparison. Although any consistent deflation of the two series of nominal values will show similar movements of productivity and compensation, it is misleading in this context to use different deflators for measuring productivity and real compensation.
So, wages are not rising with productivity. Compensation is what is rising with it. This is an important distinction many of the above articles do not seem to get.
Before we move on let me drop a very informative article on the subject: http://www.forbes.com/sites/scottwinship/2014/10/20/has-inequality-driven-a-wedge-between-productivity-and-compensation-growth/
As an aside, it's relatively inherent in the nature of inflation that the value of the minimum wage will decline in real value if inflation rises and it stays constant. But the minimum wage isn't exactly the discussion I thought we were having.
Anyway, let's look at low skilled workers. It doesn't necessarily follow that, while productivity in the economy as a whole has increased, productivity has increased as much, or at all, for every sector, industry, firm, and worker. It's certainly possible for productivity to decline in some cases. I imagine it's hard to get data for firms, and we currently can't measure productivity for individual workers, but different sectors/industries are a different story.
If we take a look at the stats, one can see that different industries in the US have experienced very different growth in their productivity:http://www.bls.gov/spotlight/2013/productivity/
This paper, while looking at the UK instead of the US, seems to support this conclusion about productivity being unequal in an economy: https://www.nber.org/papers/w13351
This article also seems to support the idea that productivity is different across sectors: http://esoltas.blogspot.pt/2015/09/inequality-and-productivity.html
To quote Soltas:
35 percent of the variance in the change between 1987 and 2013 in sector-level log hourly labor compensation is explained by changes in log labor productivity over the same period. A one-percentage point increase in productivity generated a 0.41-percentage-point increase in compensation.
As an aside, the data on the research on this seems to be a bit sparse, and I don't necessarily think it's very helpful for me to go digging in articles on JSTOR most of the people here can't access.
So one comes to the conclusion that productivity is unequal across the economy, which could (and seems to, at least from my perspective) explain, to an extent, differences in compensation across the economy. I wouldn't venture to claim it's the only factor. Also, the fact we (and economists, policy experts, etc) are still having a debate on this shows it is an open question that has not been settled yet. It's also obscured by the imperfection and incompleteness of our data and measures, differences in controlling for inflation, the political biases of the people having the debate, etc.
I must state again, I have made no claims here on the fairness of the situation. I'm only discussing what I believe the situation to be.