You need to separate the stability of individual large organizations over time to the relative importance of all large organizations. The Mormon faith is growing and other religions are dieing, but on average about the same number of people are part of some religion. Google grows as GM dies, but the average number of people working at large 5,000+ person companies seems fairly constant. Individual government organizations grow and die but overall the government workforce seems fairly constant. Companies with less than 5 people are a wold apart from company's with 50 but after 5,000 it's all about the same mess.
PS: The Pentagon is just an office building NORAD is far more important.
There is only one Google, but there are many crumbling behemoths. A few years ago I read a statistic about the percentage of the workforce employed by large traditional corporations, and it had continually dropped; but like a lot of statistics, it was not clear how it accounted for the trend in hiring temp or contract workers through third party front firms.
While the stability of large organizations over time, and the relative importance of all large organizations, are separate concepts, both are dropping. While Mormonism or other religions may grow and shift, in general the trend is toward the less centrally organized sects, and the big centrally organized, heirarchical ones are becoming less so, and becoming more run by the lower levels of the organizational pyramid.
Of course the Pentagon is not just an office building. Any reasonable person would believe that one of the hijacked airplanes could have been piloted into a NORAD installation if that had suited Al Qeada's purposes, but NORAD is only useful against other dying behemoths of giant organizations, such as the soviets, and thus isn't nearly as important as it used to be, and would never be bothered with by Al Qeada.
I think the reasons that we did not catch or kill Osama bin Laden at Tora Bora are exemplary of the ways that giant organizations fail. We believed we were strong enough to pursue other goals at the same time (Iraq, various shifts in policy under the cover of the Patriot Act, etc) and thus tolerated various internal groups siphoning off resources to persue those goals, and when things did not go as expected, we could not move fast enough to get back on track, and the internal groups had grown too powerful to stop. If we ever catch Osama it will probably be because we pay someone else to do it for us; I think that is loosely analogous to how IBM had to pay Bill Gates to write DOS for them, because their own internal politics and bureaucracy made it impossible for them to themselves.
One bullet point I left out of my list above, is higher educational institutions. I remember in the early days of slashdot, the education career questions were all of the type "should I go for a Phd. or settle for a Masters" or "the place I want to attend had Computer Engineering instead of Computer Science, does that matter" and stuff like that. Look at the educational career dicision questions on slashdot or here these days -- it is all variations on "should I drop out" "how hard is it to get a job with no degree" and so on.
PS: The Pentagon is just an office building NORAD is far more important.