How to continue music slides in Keynote

There are a couple of steps to this, and it's not entirely obvious.

The first is that you need to place the audio/music on EACH slide that you want it to play across.

Then you need to make sure the Play Audio Across Slides option in Inspector -> Audio is enabled:

Now, IF the same audio track is on all slides, AND the Play Audio Across Slides options is available, the track should continue to play through your presentation.

If the audio track ISN'T present on the next slide, then the audio will stop when this slide transitions out.

If the audio track IS present on the next slide, but the Play Across... option is not selected, then the audio will restart from the beginning.