This is a minor bug and a bit tricky to reproduce. To reproduce: Activate and deactivate the thaumostatic harness while wearing the cloudstepper ring. The harness will randomly stop producing sounds. Also this often occurs when the harness runs out of power or landing and then immediately jumping and flying again. If the cloudstepper ring is unequipped, sounds return to normal. I couldn't reproduce this bug without the ring, so the ring is definitely messing with the sounds of the harness.

So is it only the flying loop that is not working, or does this also apply to the sound that plays when it is disabled? In any case, I have to check if there is some kind of sound limit or similar that can cause this.

Edit: actually, I don't think this is a sound problem - instead I think that the issue is that the amount of Vis in the harness is not syncing to clients when needed, so it thinks it has 0 vis, which will not play the sound. Try opening the baubles menu when you get the sound issue - that should sync the harness and make the sound work if my theory is true.

After testing for some time, the sound works again after opening the baubles menu so I think your theory is correct.

Edit: After testing extensively the sound comes back every single time, so I can say with 99% confidence that what you proposed is correct.

Now that I've experimented more it tends to happen when activating and deactivating while there are other sounds playing (I was in a nether fortress where there is constantly fire crackle from blazes). Also unequipping and re-equipping the harness fixes the sounds. My (bad) guess is that a sound playing at the same time breaks the harnesses sounds.
Edit: It also seems to break when loading chunks.

After playing a lot more I don't think it necessarily breaks when using the cloudstepper ring, it breaks quite randomly and inconsistently.