There are two problems with the OP's original question(s)

First, it's necessary to recognize that by asking, Is classical music still relevant today?, followed by, Does classical music still have a place amongst today's audience, or has it been relegated to more specific listeners (i.e. music students, people learning instruments, elderly people)?, you're essentially asking two entirely different questions, because the popularity of classical music has little to nothing to do with it's relevance. You have a non sequitur on your hands; It's akin to asking, Did you pack your lunch today, or did you walk to school?

Secondly, we don't have an accurate definition of what classical music is as it pertains the question. Is classical music music that has been composed through standard musical notation? Well, we know that almost all genres and styles have used that method. Is it music that has been composed for orchestral ensembles? We know that a lot of classical music was composed for smaller ensembles and solo instruments. Are we talking about a particular type of instrumentation? We know that classical music has been written for just about every instrument that has ever existed, including electric guitars and synthesizers. Are we talking about a particular time period? We know that classical music has continued to be composed from about 1000 AD until today, even though, ironically, we use the term classical as a catch all term, when it more specifically denotes an era of music between 1730 and 1820.

For all intents and purposes, all contemporary music is classical music. most of it just happens to use a more rigid, restrictive set of compositional criteria. So, classical music is almost comprehensively relevant. End thread.

I don't really mean end thread. I'm just being antagonistic.

Mozart's use of circle of fifths at 1:10 in this sonata sounds super contemporary and jazzy and ahead of his time. And while that's not exactly an argument for yes... yes, classical music is still relevant.

I'd say yes and we must admit that classical music has an huge impact on music in general.

Yes because it's better than other music.

If you mean contemporary "classical" then no.

I still bump it on my way to work in the AM depending on my mood.

Yes, more than ever. Considering the downhill trend of American music since the 90s. Nothing much is really worth listening to now except classical music.

Classical music is super relevant and has a huge social role. It carries the responsibility to translate/describe with music how life is like in a certain historical period and geographical spot. I mean, when you listen to Bach you can picture yourself in a church in Germany, you can feel religiosity, you are transported to the 17th/18th centuries. Likewise when you listen to Shostakovich you can feel the tension, the madness, despair of the years of war and uncertainty in Soviet Union. You always can tell (briefly) when the piece was composed just by listening to it.

It's just like painting. Now people have cameras, photography. And we have rock, pop, blues, etc ad infinitum. Still, the precursors are relevant and of course can't be left aside.

I agree with Duga and Driveyourcardowntothesea
 

Yep, classical was a cultivated art form, but the basis for so much modern music because it so rigorously and thoroughly explored musical possibilities. It was like the transition from alchemy to true chemistry.

As for getting bored with it, yeah, maybe not enough variety of exposure? I personally can listen to more Romantic era stuff than Baroque any day, much as I love Bach. I need the emotional dynamics. Of course, some of this was due to advances in musical instrument technology, but then, that was driven by the demands of composers like Beethoven!!

And don't forget, Franz Liszt's Hungarian Rhapsody No. 2 has been incorporated into far more cartoons than any other piece of music ever! Especially Warner Bros.' Rhapsody Rabbit and that Tom and Jerry knockoff.

Laws of nature
 

Darwinian theory states that you must adapt to current needs. This is true of everything. If classical music does not look to the future and adapt accordingly,it can not survive. It will die a long and painful death. At the moment it is not even sickly! Even though it is being dwarfed by it's neighbour pop,rock... music. All around the world there are thousands of 'voluntary' performers in thousands of amateur music groups and their enthusiasm is not waning. There are hundreds of professional orchestras around the world even though budgets are tight. It is a tough old world out there but there is no real evidence that classical music has become irrelevant. But will in the future have to become more adaptive.