I was able to make a test page with a menu applied to it and a spry collapsible panel. I set the default of the panel to be closed. When I test this page the spry panel defaults to a closed state and when I click on it the panel opens.
When I viewed the pages on your site I was able to interact with the menu on the page but I did not see the spry objects to test. What is the specific menu you have applied to the page and what is the specific spry object on the page? I will do some more testing to see if I can find an issue. On the site you posted a link for how can I see this behavior occurring?