Yeah, we ended up just hacking functions.php, forcing the is_ssl() function to always return true. Funny we both used this same plugin and thought the problem might be related.
However, this issue has nothing to do with the ADI plugin.
Do you use an SSL front-end (instead of doing SSL on the apache server running WordPress)?
I’m having the very same issue with this plugin after upgrading to 3.5.1. Restoring from backup (both wordpress files and database) was the only way to fix it. I cannot upgrade WordPress until this problem is resolved (or I stop using the plugin, I suppose).