Honest question: Why do you think that generalized and specialized AI are distinct things? Is it not possible that general AI is a specialized AI applied over the field of specialized AI generation?
AI problems can be characterised as those where there's no clear path to a solution (otherwise we just call it "programming"); tackling them necessarily involves trial-and-error, backtracking, etc.
Since there are far too many possibilities to enumerate, solving such problems requires reasoning about the domain, e.g. finding representations which are smooth enough to allow gradient descent (or even exact derivatives); finding general patterns which will apply to unseen data; finding rules which facilitate long chains of deduction; etc.
The difficulty is that there's usually a tradeoff between the capability/expressiveness of a system, and how much it can be reasoned about. If we choose a domain powerful enough to represent "the field of specialised AI generation", for example turing machines or neural networks, methods like deduction, pattern-finding, gradient following, etc. get less and less applicable and we end up relying more on brute-force.
To me, this is where the AI breakthroughs are lurking. For example, discovering a representation for arbitrary programs which allows a meaningful form of gradient descent to be used, without degenerating into million-dimensional white noise; or to take deductive knowledge regarding one program and cheaply "patch" it to apply to another; and so on.
There was a great article recently on HN that highlights the current problems:
http://www.theverge.com/2016/10/10/13224930/ai-deep-learning...
https://news.ycombinator.com/item?id=12684417
Just because we may acquire the processing power estimated to be used in the brain (in operations per second) doesn't mean we know how to write the software to accomplish the task. It is very clear current algorithms won't cut it.
Also, I think we are a few orders of magnitude off on raw processing requirements because I think it is a bandwidth issue as much as an operations per second issue.
TL;DR - you could throw as much processing power and data as you want at any current deep NN or their derivatives and you wouldn't get general intelligence.
That said I don't think the winter will be as bad as before because, like OP says, specialized AI is useful.
I think a lot of the early AI research (not my specialty) had the idea that if we made a bunch of systems that were good at their own piece of the puzzle, then we could just tack them together and get real intelligence. It just didn't turn out that way. Something I'm more familiar with is graphical models, and while they in principal could do amazing things when you stick little expert components together, we've proved the complexity grows pretty badly in the most general cases that would have been really amazing. I'd bet similar things happened in other "let's put a bunch of specialized systems together" tracks. Maybe we can do it, but not the naive way that would have been great.
Then you can get interesting and philosophical about it, where you might even say that emulating intelligence and intelligence are different. Like the chinese room thing, or even a character in a story vs a physical person. I'd rather not weigh in on that right now, but there are good interesting arguments both ways.
This would be a very surprising result. For example, if I can make a TSP-solver-emulator... I have a TSP solver.
General AI - think about thinking machines
We can do the former, have no clue how to do the latter.