The demo page on Dynamic Drive works fine here in FF 3.0.5. Is that what you meant by "your copy of the script"?
However, with persistence turned on, whatever the state of the menu on unload of the page will be the state when returning (this includes merely refreshing) to the page, unless the URL parameter is specified.
Persistence will have no effect at times in Opera, which doesn't fire the onunload event in the same way as other browsers, or in any browser that doesn't support cookies. IE 6 'standalone' doesn't support cookies. What type of IE 6 do you have?
If you want more help:
Please post a link to the page on your site that contains the problematic code so we can check it out.