The median wage has increased fairly steadily since WWII. But for the past three decades or so, it's entirely due to the improving status of women in the workplace. That's good news, of course, and it's also good news for family incomes, but there's a flip side: the incomes of men really have stagnated. If you compare apples to apples — men aged 35-44 working full time — median income doubled in the three decades after WWII and has declined in the three decades since then. If you add in benefits, growth has been about zero.
source

If you're really interested, I provided the source. If you link back a few links you get to the actual study.

But what are the economic reasons behind the change in the growth trend? For example, given the US has traditionally been reliant on a long tail of the low skilled, is it the result of further changes to the skills distribution?

I always find bargaining arguments difficult. I'd be happy with reference to  bargaining power and overall compensation, given we can just refer to the redistribution of economic rents from employer to employee. However, reference to median compensation is less clear-cut. For example, trade unionism may well just reinforce wage norms. This would effectively refer to redistributing wages "between" employees. The crucial empirical work then becomes testing the union impact on the wage distribution (i.e. isolating the trade union effect on income inequality)