I think this is a great question; it’s certainly one which has been asked often in the past 120 years.
A number of previous answers have, correctly in my view, pointed out that no-one can really tell. Some composers we know well took time to reach their position, others arrived very quickly.
I do think that Robert Holmen is wrong in saying that no-one has the significance of Beethoven, Brahms, or Stravinsky. There are plenty of composers who made a big splash when they were young. Peter Maxwell Davies, for one. Birtwistle for another – people walked out of the premiere of Punch and Judy. There are also composers whose music has become massively popular like Gorecki or Pärt. There are others who have crossed boundaries, especially between concert hall and film, such as Philip Glass, Michael Nyman. Others still who have crossed genres like Mark Anthony Turnage or Wynton Marsalis.
In many ways it has become more difficult to break the mould in the way that composers such as Beethoven or Stravinsky did. Our musical language is so pluralistic that new ideas are the norm. Indeed, for some time during the 20th century, to not remake your compositional language with each new piece was regarded as a failure.
The seismic changes in musical language that occurred during the first quarter of the 1900s reverberated throughout the century and we are still in a fantastically fluid and febrile creative period.
Despite what many listeners believe, there is a huge amount of new music being written and being performed. According to data gathered by the Baltimore Symphony, in the 14/15 season in the US, nearly 12% of music performed by the top 22 orchestras was by living composers.
Pieces like Adams Harmonielehre and Short Ride in a Fast Machine, Skempton’s Lento, Pärt’s Cantus in memoriam Benjamin Britten, as well as operas by Glass do get performed a lot.
I am absolutely sure that many of the pieces written today will be listened to and performed again in the future. I don’t think we can say for sure which ones, but I’m certain that musicologists will look back at the period from the late 20th to mid 21st centuries as one of the most exciting and fertile in all musical history.