Pretty much the *only* survey reporting a long-term decline has been the General Social Survey conducted by the University of Chicago, which is expressly non-anonymous, conducted via in-person interviews, funded by gun control advocates (Joyce), and run by a gun control advocate. Ownership rates assessed by Pew, Gallup, and others in anonymous surveys are much higher, and actual hard data (e.g. firearms possession licenses, in states that require them like IL and MA) show increases, not decreases.
Boston Globe - Gun licenses on the Rise in Massachusetts
Illinois FOID License Holders Up 33% 2009-2013
FWIW, the FOID numbers have kept rising; I believe the number of active Illinois FOID cards as of 12/15/2015 was 1,942,008, which would be a 54% increase in FOID cards since 2009, if I have that number right. And since FOID cards correlate 1:1 with on-the-books legal ownership in IL, a 33% (or 54%) increase in valid FOID's is a commensurate increase in licensed ownership---in the GSS's own backyard.
I'll point out that these are both heavily Dem, deep-blue states, but the same trends are at work in other blue states, as well as purple swing states and red states, whether you look at all the available proxies for ownership or at anonymous self-reported ownership.
As of 9/2016, a Pew Research Center poll put the number at 44% admitting to a gun in the house, 51% saying no gun, and 5% refusing to answer the question. A 1/2016 CNN poll put the numbers about the same, with 40% saying yes and 9% refusing to answer.
Carry licensure, which isn't correlated 1:1 with ownership but is still loosely correlated, has more than doubled since 2007 and IIRC roughly quadrupled since 1999.
WSJ - Permits Soar to Allow More Concealed Guns
Here in eastern NC, my local shooting range is now jam-packed every time I go there, when it used to be fairly sparse years ago, and I have a lot of coworkers and friends who bought their first gun within the last few years, including a longtime coworker who bought his first two months ago.
It is an article of faith among gun control advocates that the GSS is the only reliable measure of gun ownership, but if you look the totality of the metrics, including hard license data, overall ownership trends do not appear to be moving in the prohibitionists' favor. And it is incontrovertible that the styles of guns people have been buying in the last 25 years are not favorable to gun control advocates' handgrip-shape and magazine-capacity crusades, either. As I mentioned upthread, the market has been moving strongly away from larger calibers and straight stocks, toward the modern-looking centerfire .22's and double-stack 9mm's that the gun control lobby wishes to ban or severely restrict.
Perhaps it is hard to see from within the cloistered DC/NY/CA bubble, but Bloomberg et al are trying to outlaw guns and magazines that are legal in Canada and much of Europe, the banning of which would be considered a serious violation of the social contract across much of the United States. If your bans have gotten only 5% to 10% compliance among owners in New York and Connecticut, just how well do you expect those bans to play in NC, WV, Texas, Ohio, Tennessee, Florida, or Michigan? It is hard to express just how repellent the NY SAFE Act and similar crap is in states with a strong culture of lawful ownership.
FWIW, there were warnings of the flaws in the current approach in Virginia's 2015 state senate races, which IIRC handed control of the Virginia legislature to the repubs:
Washington Post - Did gun control cost McAuliffe and Democrats the Virginia election?
Too bad no one inside the bubble was listening.
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