private var st:SoundTransform  = new SoundTransform(0);
private const max:int = int.MAX_VALUE;
private var context:SoundLoaderContext = new SoundLoaderContext(2000, true);
private var bkdSound:URLRequest = new URLRequest("background.mp3");
private var bkdS:Sound = new Sound();
private var pausePoint:Number = 0.00;
private var paused:Boolean = false;
function init():void{
   bkdS.load(bkdSound, context);

   //START PLAYING THE SOUND
   bkdChannel = bkdS.play(0, max, st);
}

function pauseSound():void{
   if(!paused){

   //THIS PART IS THE KEY YOU NEED TO % INTO THE LENGTH OF THE SOUND
   pausePoint = bkdChannel.position % bkdS.length;		
   bkdChannel.stop();
   paused = true;

   }else{

   //USE THIS TO RESUME//
   bkdChannel = bkdS.play(pausePoint, max, st );
   paused = false;

   }
}

There is a bug in AS3 where when you pause a looping mp3 the saved position gets messed up because the length extends with every looping instance.

fix for looping sound pause issue in AS3

ActionScript 3