Funny... works for everyone else...
If you'd read around a bit you would know that this has been an issue for a number of people. Another issue is the sound becoming badly distorted after alt-tabbing out of the game, got this myself and it only happens with Elite. There was a thread about it in the support forum but nobody has figured out what the problem is, hopefully they'll sort it out eventually.
That said, agree with the OP that sound design in this game is exceptional. Somebody mentioned Alien: Isolation as being another game with great sound that possibly beats Elite. While A:I has some very atmospheric use of sound it doesn't have the same palette and depth in the design as this game (imo etc).
One thing I love is that once in a while a ship you are very familiar with will make a noise you simply have not heard before, due to whatever combination of maneuvers and systems you are using. Flying my Cobra recently I hit boost then threw it into a tight rolling turn, the noise it made sounded like a combination of a Wookie howling and Tie Fighter screeching... put a massive grin on my face and despite trying I have not actually been able to get the exact sound out of it again to record.