Rief, are you using savestates? If so, try saving/loading from memory card instead.
Just noticed this issue for the first time while loading up a Final Fantasy Tactics savestate.
I can boot the game and it plays sound just fine, but loading a state cuts it off completely, both music and sound effects.
But I just took your advice and did a normal save in the game, then loaded it from the memory card. Sound was working fine. Did a savestate, quit FPSE and loaded the savestate and now sound is working even using states. Very odd. But at least there is a fix for it if it happens again. Thanks for the suggestion!