It's annoying, but it's no huge problem. It's interesting, actually, to listen to what the battle sounds like without the music. I've noticed this in a couple of dungeons in CL as well. It's not a huge deal though.
I noticed this also. There is music during the first battle, but after that, in each succeeding room of the gauntlet tower, the battle music does not play. This bug was consistently happening in all gauntlet towers. The bug always began after completion of the first battle and extended to all remaining battles in that tower.
(Frankly, I enjoyed the silence, lol. But I suspect this is a bug and KI will want to do something about it eventually.)