I am fairly sure that being knocked down in the middle of playing Fascinate or Enthrall does not interrupt the song -- it completes and mobs get fascinated. Last night however, as far as I could tell, getting stunned in the middles of playing Dirge made the song ineffective -- the song completed, but mobs took no damage from it. I think a message along the lines "you cannot do this while stunned" was flashing, but with all the fireworks on the screen it was hard to tell. I managed to escape, shrined, came back, and those same mobs did take damage from Dirge, so it was not mob-specific.
Are all songs interrupted by stun, and not interrupted by knockdown?