Basic models of political economy hold that inequality self-corrects. As income concentrates among a smaller group of voters, majorities will vote for more redistribution.
But that isn’t quite how the world works. For starters, the poor vote less than the rich. And they don’t vote exclusively based on their economic self-interest. Many Americans, rich or poor, mistrust government. They support free-market capitalism [which isn't in the middle or lower class's economic self-interest] and view the distribution of the nation’s economic fruits as roughly fair [because they don't know history and don't understand how they've been duped by the super-rich plutocrats, the anti-small-d democrats].
The growing concentration of income can, in fact, make inequality more difficult to correct, as the wealthy bring their wealth to bear on the political process to maintain their privilege.