I've been reading some of the responses to the claims by Wendell Cox and Joel Kotkin that the newly-released Census 2010 population figures fail to show a predicted "return to the city" by suburbanites. Ryan Avent points out that given central city supply constraints, what we should be looking at is not only population figures but also housing prices to determine where changes in demand have occurred. Indeed, Austin Contrarian's Chris Bradford identifies core Austin neighborhoods which experienced increases in both price and total housing units over the past decade while simultaneously losing population. Michael Lewyn notes that a city-wide view fails to capture what may be very positive changes in those individual neighborhoods with truly urban form. Stephen Smith writes that given the long time frames involved in urban population shifts, it is far too early to be writing an obituary for the American urban renaissance.
I have a couple thoughts to add to the points made in the above comments (which are worth reading in full). First, the academic literature examining gentrification and urban revitalization typically focuses not on population gains, but on 1) average incomes of residents; 2) educational attainment of residents; and 3) as mentioned above, changes in housing prices (see here or here for example). Population changes are not a good proxy, as, for instance, the process of population loss frequently can be associated with neighborhood reinvestment (the "un-slumming" process described by Jane Jacobs).
Second, the near-ubiquity of restrictive zoning in American cities has produced distinctive patterns of development in many urban areas. Limitations on commercial and office use produce intense competition among businesses for scarce downtown land that crowds out residential uses, while immediately outside the core single-family residential housing in a largely sububan format predominates. The result in most places is a small downtown of parking lots and office towers surrounded by vast expanses of low density residential (see Phoenix, Little Rock, Charlotte, San Antonio). In such a setting, what does it really mean to "return to the city"? One's choice may be between a new, large, cheap single-family house in a non-walkable suburban jurisdiction with good schools and low taxes, an old, small, cheap single-family house in a non-walkable streetcar suburb (minus streetcar) in a city with poor schools and high taxes, and (possibly) a new, small, expensive condo in the neglected downtown of the same city.
By contrast, those relatively few high-density, walkable urban neighborhoods that exist in American cities have rapidly revitalized, even in cities otherwise losing population. Just in the past ten years, off the top of my head: the formerly gritty industrial neighborhood of Lawrenceville in Pittsburgh, blessed with narrow streets and brick row houses, Point Breeze in Philadelphia, and Fort Greene in Brooklyn. I'm sure there are many more. A list of urban census tracts indexed for urban form might confirm the very strong anecdotal evidence on this point.