Well, that's the extent of my knowledge with Autoplay, I'm afraid. But some more details might help others be able to answer better:
Are you publishing as SWF or HTML5?
Do you experience this when previewing the project? When viewing it locally? When viewing on a server? Running the SWF file alone, or running the SWF file using its html file? On a particular device? All of the above?
Is this a problem with particular projects, or does it happen when you create a new project?
What specific versions of 6 and 7 are you publishing from?
There's also this thread which might be worth a look if you're experiencing the problems with HTML5: http://forums.adobe.com/thread/1148299