Classical music is dead (or nearly so) because of the dearth of popular, living composers. There is no popular element in what modern composers produce, and they have virtually no desire to please popular sentiment. Indeed, these are qualifications necessary for them to ever be considered "serious" in the first place. Ultimately the problem lies with the artistic deadend the genre has reached and with the composers. The neglect is fully earned.
Here's the fundemental problem: The fact that the genre we know as classical music is entirely sustained by past masterpieces. Until living composers--through their music--inspire the classical audiences to place the same faith in the modern output as they do in the classics--we will always be lamenting the Death of Classical Music.
This is along my line of thinking, but with a significant difference, in that I am not willing to put the entire blame for our present impasse on composers. A composer is under no obligation to please his or her audience; in fact throughout history the composers who have survived have been the most demanding and original voices, those who most followed their inner ears and imagination (Mozart, Beethoven, Wagner, the later Verdi, Debussy, Stravinsky, etc.). Eventually through repeated exposure, the idioms of these composers have become familiar to audiences and absorbed. But composers who write primarily to please (such as Cimarosa, Paisiello, Meyerbeer, Adam, etc.) eventually are forgotten or played far less because there's less substance in their work to sustain repeated listening.
Several events occurred simultaneously in the early 20th century that have led to the current impasse: for one, the musical idiom, primarily as developed by Schoenberg and his followers, and later by composers such as Boulez and Stockhausen, became more complex and forbidding than ever at precisely the same time that a canon of accepted works was falling into place. At the same time, largely due to the phonograph, composers from the past became more available than ever to listeners, often in multiple excellent performances of the same work. As a result, music has turned into a museum, where each listener can experience his own selection of masterpieces at the flick of a button, and if he doesn't like Carter or Ligeti, he can put on Tosca or the Ring.
There is another, in my view undesirable, offshoot of the easy availability of recordings, and that is the decline in amateur music making. Households 100+ years ago generally owned a piano, and at least one member of the family played. Symphonic works were learned not from recordings but from playing 4-hand arrangements. By contrast the music consumer of today experiences music in a more passive way, and is less familiar with the materials of the musical language. This situation needs to be rectified as much as the crisis between composers and listeners.
I don't blame audiences for not accepting the more advanced music any more than I blame composers for composing it. But this particular impasse remains, and turns inside out the older norm of a musical culture that (as in popular music today) had been sustained primarily throughout history by new creations. To that degree, there definitely is a problem, but it's not one that can be solved by composers writing "what the audience wants" - as any composer with a strong, original voice runs the risk of not being accepted immediately.
But at the same time, I'm not convinced that classical music is "dead," whatever that means. Most likely in fact there are more people throughout the world who take an interest in classical music than ever before. (Any performance of the Eroica in New York or London will be experienced by hundreds, maybe thousands of people, any of whom can buy as many recordings of this work as they want. When Beethoven premiered the work around 1805, only a couple of dozen aristocrats heard the symphony in a nobleman's palace.) For example, the spread of recordings has led to greater interest in Western classical music in parts of Asia - apparently not so much in India, but probably most of all in the major cities of China and Japan. There are upward and downward trends here and there, just as in the stock market, but overall the likelihood is that classical music is more available to and more listened by more people than ever. Opera, for example, is doing quite well, certainly better than ballet, though on the other hand neither classical music nor ballet is approaching the current popularity of art museums - where one is not chained down to a seat and can walk around, concentrating on the paintings one most likes.
But there's a certain satisfaction arising from the self-pitying complaint that "classical music is dead or dying"; one feels at once a member of a beleaguered minority and a member of a chosen elite.