As you should see, it's not really that simple to say "39% stay and 61% fall out." While technically correct, falling isn't equally distributed over the other quintiles. The children of the top quintile are only 9% likely to fall in the bottom quintile and the children of the bottom quintile are only 6% likely to rise to the top quintile.
And really, the top comment was trying to claim the parents migrated income brackets. The numbers here are about children inheriting the incomes of their parents. This data strongly suggests the wealth gains over the past decade are in fact concentrated in the already wealthy. Not only that, but it shows the concentration of wealth has momentum that lasts for generations.
The United States today still has tremendous opportunity for income mobility compared to many other parts of the world and other parts of history. But these articles are showing a disturbing trend that this may not be sustainable.