Also arguably the US's republican model has had some of the weakest "democratic" aspects. Its popular veneration of the President as a martial pseudo-king "Command in Chief" (very weird to watch from up here in Canada, BTW, esp during the Bush post-9/11 years), its blatant blurring of church & state, its obsession with its military, its overt and obsequious patriotism and national chauvinism, its expanding federal powers, its imperial ambitions (both internal to the Americas and then even further abroad after WWII), its history with slavery and racial discrimination, etc.
It's a contradictory country. On one hand having some of the most radical and egalitarian motive forces, and being earlier to the democratic impulse than most of the west. On the other hand having ossified authoritarian impulses built deep into its system.
I think you'll find more healthy democracies in western Europe and Canada, though they don't have the same radical liberal (small, classical l) ideological underpinnings.
Adams, Harrison, Roosevelt, Kennedy, Bush, Clinton. That spans the entire history of the country, and doesn't leave much room for cycles. I can't think of any period when inherited wealth and connections weren't extremely helpful in a political career.
I'd say that "ossified authoritarian impulses built deep into [the] system" is a global issue, not a uniquely American one.
A better answer is that contemporaneous class systems elsewhere in the world were so rigid, early in American history, that merely not having formal orders of nobility seemed shockingly egalitarian. Two and a half centuries later we're less eager to pat ourselves on the back for somewhat-better-but-only-somewhat levels of equality. But failure to make enough progress is not the same as regression.
But to stay on topic, I believe it was Churchill that said democracy was the absolute worst form of government. Except for all the others.
If this is an indicator, how long has the U.S. political system been failing? John Adams was the second President starting in 1797. His son became the sixth President in 1825.