New York has remained the largest U.S. city (metro area) for some time. It has had its ups and downs, of course, but it has found ways to remain top dog. Nothing succeeds like success.
The March 2007 American Economic Review includes a splendid paper by Giles Duranton, "Urban Evolutions: The Fast, the Slow and the Still." He shows that three prominent urban phenomena plausibly coexist. He even has an economic model that explains it all. He utilizes the idea of agglomeration opportunities and their relation to city size.
Yet, these are actually realized when efficient location patterns are allowed to emerge. Having said that, one has to admit that the top dog metros (by definition) have done this best.
Here is the Duranton's abstract:
With the use of French and US data, new and systematic evidence is
provided about the rapid location changes of industries across cities (the
fast). Cities are also slowly moving up and down the urban hierarchy (the slow),
while the size distribution of cities is skewed to the right and very stable
(the still). The model proposed here reproduces these three features. Small,
innovation-driven shocks lead to the churning of industries across cities. Then,
cities slowly grow or decline following net gains or losses of industries. These
changes occur within a stable distribution. The quantitative implications of the
model are also explored.