Actually, I don't recommend embedding MP3. My recommendation was putting a WAV file into the library of Flash Pro and exporting it as SWC (or you could export a SWF too, which could possibly be loaded at runtime). Flash Pro converts the WAV to MP3, but somehow, it can play back without the silence that other MP3 encoders like Lame add. In my experience, music will loop seamlessly this way.
I usually use Sound's play() with a loop count set to int.MAX_VALUE, if I want it to repeat indefinitely. I've never tried manually playing again on Event.COMPLETE, but I definitely wouldn't be surprised if that added a gap.