I know facebook does uses HTML5 media element for example when displaying media content to a journal on iPad.
First I would check the audio tag you are using works on a blank HTML5 page (just to be sure there is no issue with the file/server you are using).
Could not it be that just the autoplay or loop attributes are not supported? We know that Apple disables autoplay on all of its mobile devices. Maybe facebook has rolled out something similar.
Try something like this to see if it plays on user interaction:
<audio id="backgroundMusic" controls>
<source src="sounds/startTheme.mp3" />
<source src="sounds/startTheme.wav" />
</audio>
To check if HTML5 audio is supported in an environment you can use:
function supports_audio() {
return !!document.createElement('audio').canPlayType;
}
More information on this here.
Otherwise good old flash can be a fallback option.