by the way, we used flvplayback component in flash as3. so flash publishes both the flvplayback skin swf and the main swf of the FLA file. Then on Captivate's side, after zipping, we included the swf files there.
Hi, did you ever get an answer to this question? I am having the same problem and cannot figure out a workaround. When I preview the project, the animation stops when I click Next, but when published, the swf continues to run in the background as you are describing.
Yup, in the swf animation I placed some lines of code to make the slide pause but in my case since I'm playing a video on my swf pausing the slide doesn't pause the video.
myRoot = MovieClip(root);
mainmov = MovieClip(myRoot.parent.root);
mainmov.rdcmndPause = 1;
The code above will pause the slide. You can try if it works for you.