Personally I think one of the major reasons for the decline of classics is precisely the one identified by Hale is his quasi-famous-round-here "Art of Reading Latin" article/speech, written well over a hundred years ago - it seems to take far, far too long to learn the languages, and be far, far too much effort for too little gain.
Put plainly, Latin and Greek are very, very badly taught; I don't mean, however (as one or two other posters said) that we should half-abandon grammar and wax communicative about our daily routines a la French (the communicative method destroyed my chances of learning French - I'm now starting on it afresh with a wonderful book from the 1930s that is so old-fashioned and grammatical that it introduces the past historic/preterit/simple past before the perfect.)
I went through seven years of Latin in school (interspersed with a couple of periods of home-education which didn't really change anything on the classics side of things) - and at the end of that, I could barely read a thing. I started off really enjoying it, but my interest waned as I kept getting nowhere, even after "completing" the "grammar". By the last couple of years, I could barely wait to get away from it - and yet now I'm re-teaching the languages to myself, my interest has undergone a sudden revival.
This lack of progress in school was primarily because classics teaching generally makes the languages far more complicated, and difficult to remember, than they need to be. One of the best examples: imagine my surprise when I came back to Latin recently, after losing most of it, and found that it's possible to learn the entire regular Latin verbal system without learning a single full paradigm. Even esse (and hence also posse - my school-taught latin made no attempt to point out that these two verbs are related) are much, much more regular than I ever suspected. It's perfectly possible to learn the entire regular system in no more than a week (I did it in two or three days, but then I had some latin to start with). Even slow-paced courses would take no more than five or six weeks. And yet I spent two or three years on the verbal system in school (interspersed with other things of course), learning a paradigm of every tense, often four times for each conjugation, which makes it incredibly easy to forget (the subjunctive never really stuck with me). Now I can look at almost any latin verb, even if I don't know what it is, and say exactly what it can and can't be, simply by analysing it morpheme by morpheme - it may not sound like much, but one or two weeks of learning the system properly was more effective than seven whole years previously.
My classics teachers were for the most part very sincere, and most of the time good teachers. But they simply had no clue that maybe they should re-analyse the old teaching methods, stop telling people the gerundive meant "requiring to be", notice the the verbal system was far more regular than they thought, and so on - Classics has always been an intensely traditional thing, mostly for obvious reasons. Some of this is harmless, if annoying (writing prefaces to critical editions in Latin and so on), and some of it is devastating (like the abovementioned clinging to incredibly bad teaching methods).
The decline of writing in greek and latin is also a reason for people not getting a good command of the language; the scanty "English-to-Latin/Greek" (as composition is now called on the eastern side of the Atlantic) sentences we did in school were next-to-useless. But the old method of "any construction not used regularly by Cicero, Caesar or Livy will not be admitted!" with teachers forcing people to translate incredibly boring passages from the dregs of the imaginitive output of the human race is hardly something to look back to as a glorious time.
But in the end I think the greatest reason for the decline of Latin in schools is because it is taught in schools - places intentionally designed to stop people thinking for themselves, when Classics is precisely the sort of discipline that needs that most. Schools are also very good at teaching people that it's never worth doing anything you won't be examined on, and I don't blame people who have been throught the school system for having that attitude.
In a wider sense, almost no one seems to bother with trying to understand how the languages work - they're just a hurdle to be passed on the way to greater things. No one, not the teachers, the university lecturers, the grammars, the dictionaries, pays any attention to derivational morphology for example. I learned that "pugno" was "fight" and "oppugno" was "attack". No one attempted to explain the perfectly logical and interesting link between those two and, because of the way it was taught, I never really thought about it either. It was slightly better in Greek, but not much.
Another thing, I think, is that it would be good to introduce classics students to palaeography if at all possible - so few ever are. The incredible divide most students feel between themselves and the editor of, say, an OCT might start to lessen then, and I think it would make the whole linguistic and textual side of the thing seem less daunting and monolithic. Of course this is much more difficult than it sounds, since the vast majority of places hardly have handy manuscripts lying around, but it's an idea.
Maybe the whole problem of people not continuing with classics is that they feel such a massive gap in so many ways between themselves and the "experts", far more so than in any other discipline I've come across.