Hello - I'm a musician myself, very familiar with classical music though I stopped playing it after high school.

There are so many problems I don't know where to start. I'll just list them at random.

• The field of music is far broader than it used to be.
• And music itself has much more competition for people's entertainment time. When I was young, if you wanted to see a movie, you saw it in the theater, or waited for it to appear on broadcast TV. Video games weren't bigger than Hollywood. There was no reddit, no internet.
• You often aren't allowed to dance to classical music, and if you are, it's often formal dances like waltzes that people don't know how to do today.
• You often can't drink alcohol while watching classical music.
• You nearly always watch classical music sitting down. I sit down all day, when I go out I wanna go and bounce around (and I'm turning 50 this year).
• Lyrics are less common in classical music, they are frequently not in English, and even then are fairly hard for people to make out.
• Nor do the lyrics in classical music generally speak to the modern human condition, particularly for people who aren't musicheads. For example, the heavy emphasis on religious themes in classical doesn't bother me at all as a musician because, well, I just love music - but I'm not a plastic artist (i.e. painter, sculptor) and when we toured Italy last year I got really, really sick of seeing Jesus over and over again.
• A symphony is not a financially efficient way to make music. A four-piece rock band is quite competitive with a symphony orchestra for range and expression - I'd argue that the electric bass, at least, does a better job than a row of cellos - but is an order of magnitude cheaper in cost. And a four-piece rock band is less efficient than a guy rapping over a pre-recorded tape or just a DJ.
• Because classical music is expensive and requires expensive and specialized concert halls and teachers, it has needed government money to keep it going. This money is going away, and might never be back.
• For classical music, and other branches of music that are in trouble like jazz, having an educated ear is a distinct advantage - but fewer people, particularly in the US, have that educated ear.
• Once a piece of classical music starts, you're essentially trapped in your seat - you can't wander around. Many classical pieces are "extremely long" by today's standards - many people have told me about being stuck in a seat with some classical piece that they found uninteresting.
• A lot of the orchestral music in the last 50 years or so is pretty horrid. Frankly, if I had the choice of saving all of Pierre Boulez or just one Butthole Surfers album after the apocalypse, I'd gladly lose all the Boulez - and I'd throw a lot of others onto the fire too, Elliott Carter being the next alphabetically.
• A lot of the remainder is pretty hard. I personally love Schönberg but I suspect that perhaps 10% of my friends could sit through Moses und Aron (though everyone I've ever played Pierrot Lunaire for has loved it...)
• A lot of the people who are left want to be seeing "new music" - what people call "contemporary classical". There has however been a lot of hostility to performing this in orchestras. It's very understandable, because most of the audience for classical music is older and not so receptive to this.
• There is a huge barrier to entry for new performers in the field. If you wanted to learn, say, the bass and start a rock band, you might be able to do your first gig in a few months if you worked hard. If you were rapping, perhaps less time than that. It would take you a lot longer to get good, yes - but in order to play classical music with others you need literally years of practice to get to the point of "not horrible".

It makes me very sad to say this, but I don't see this ever getting fixed. Some of the problems could be attacked, but for many others it's just not clear what to do, and there are simply too many of them.