For some reason, this has just become a problem for me as well - had been playing with GLSL, then mame.ini, then my attract-mode config, but didn't change anything I don't normally change (I think). Now the snaps audio keeps playing in the background after the game has launched.
Tried switching between Fullscreen and Fill Screen, and tried setting Minimum Run Time to 1 like the OP, but no effect.
Edit: have reverted my mame.ini completely to a backup, no change (which makes sense). but at least it rules out GLSL and my mame.ini as the problem.