The SF Bay article is a little deceptive in its choice of cities, as they tell only on story of what happened to urban (rather than metropolitan) areas in the U.S. in the latter part of the 20th Century. The proportion of the U.S. population living in urban areas has, in fact, remained somewhat stable, but don't take my word for it. Instead, take the word of the U.S. Census Bureau, which, in a 2002 report, noted that "From 1940 to 2000, the proportion of the population living in central cities remained relatively stable, while the suburbs continued to grow substantially." (p.33)

You'll note that graph shows a slight decrease in the urban proportion of the U.S. from it's 1950 peak (32.8%) to 2000 (30.3%), with the major lost of 1.4% occurring between the 1970 and 1980 census. Yet, as the linked article shows, some major demographic declines occurred in major cities. The problem is that while some cities in the U.S. were losing population -- particularly "headline" cities like New York, San Francisco, and Boston -- other cities in the U.S. were rapidly gaining in population. The losses of more established cities, in other words, were largely offset by growth in other areas. So what was happening in those late mid-century decades?

The problem is that there is no one single answer to the changing mosaic of rural-suburban-urban demographics that occurred in the immediate post-war (that war being WWII) period. The story is not so much one of urban decline, as it was of rapid suburbanization, and it has a number of factors: car ownership, the Eisenhower interstate system, G.I. Bill housing benefits, etc. All of these economic shifts were also accompanied by first by the Civil Rights Movement freeing the population from the socio-legal constraints which restricted them to particular areas (while also creating new challenges) and de-industrialization that gutted the primary economic bases of many cities, particularly those Upper Midwest and Northeast. Yet, at the same time, Western cities and "Sun Belt" cities of the South and Southwest were growing at a rapid pace for a variety of reasons (full paper). So Pittsburgh and Cleveland, for example, have been hemorrhaging population for decades while cities like Boulder, Phoenix, and Houston have steadily increased in population.

Still, your primary question remains: why did those particular cities mentioned in the article dip and then rebound? The question was actually taken on by the Kansas City Federal Reserve Bank in a 2003 paper. True to form for economists, they failed to grapple with the actual issues, instead preferring to build and validate descriptive models (for more economics burns, call my hotline at 1-900-LOL-ECON). Yet, the KC Fed did specifically address the question of why certain cities declined and then recovered. They employed a model of measuring local, metropolitan, regional, and national factors, ultimately concluding that certain rebound cities enjoyed either one of two factors: 1) Strong metropolitan areas or 2) Declining emigration to metropolitan areas. In other words, the suburbs either acted as a population supply, or stopped draining population.

Every city is going to have its own narrative in this story, but let me reference central place theory (oddly enough for the second time in a week). It's a complex idea, but the gist is that polities as singular units/identities can only extend so far before some other polity becomes the dominant influence; that's your quick and dirty introduction to the idea. If you want to see an amusing and imperfect demonstration of the idea in action, check out how Facebook fans of certain NFL teams conglomerate by region. If you want a more academic take on CPT, you can enjoy the wonder that is Hsu (2012). For a more on-point dicussion of the ideas about how urban area grow, develop, and sustain themselves, I would recommend Batty (2001), which contextualizes urban agglomerations as polynucleated multicores interacting to substantiate a singular identity with multitudinous interpretations by the panoply of actors in its realizations. I'm joking a bit, but the point is that describing and defining what constitutes a "city" is more difficult than you might think.

What is no so difficult (and here we return to the basis of CPT) is that you are less likely to interact with, or depend on, a particular urban core for socio-economic viability if its a fucking long way away. Every city has a natural limit to its growth, with that natural-ness being defined by (roughly) the need to travel to the urban core, the ease of getting there, and availability of alternatives. Again, every city cited in the article you linked is going to have its own relationship to this dynamic and the larger socio-economic forces at play. The key thing to take away from this though, is that not every city decline and not every city that did declined has rebounded. Those that did dip and resurge though, had the advantage of either unique geographic/economic placement (SF/NYC are huge cities and major ports with diverse economies) and/or had their population simply move out from the city to form an economic periphery dependent on the core (you can only located your company so far from Atlanta and still reap the benefits of being near a major city).