So the interesting question is not why economic inequality is increasing, but why for a few decades in the mid twentieth century the trend was reversed.
There are probably several factors at work here, but as someone who was around and paying attention at the end of that period, I think the key to the answer is the large corporation. The period of flattening coincides with the heyday of the large corporation.
Large corporations tend to decrease economic inequality. You can't measure individual productivity well within large organizations, and even if you could, it would strain the fabric of the organization to reward people that way. They also hide a lot of inequality by giving elite employees benefits that don't show up in their salaries (http://paulgraham.com/ladder.html).
What happened at the end of the 1970s was that the most ambitious people started to lose interest in working their way up the corporate ladder. They wanted to get paid upfront. That was why the term "yuppie" was born then. Before 1980 it was rare to find young professionals with lots of money. In the old days, they were all still paying their dues at that age.
I remember the transition quite clearly. When I was a little kid, in the early 70s, the most impressive thing you could do was to work for a large corporation. It was the era of conglomerates in shiny office towers. By 1980 we were starting to see a glimpse of the world we now live in, where the ambitious people are all free agents.