Looks like you are hitting the limit on connections per server. I see you are loading a lot of static files and my advice is to separate them on subdomains and serve them directly with Nginx for example.
- Create a subdomain called img.yoursite.com and load all your images from there.
- Create a subdomain called scripts.yourdomain.com and load all your JS and CSS files from there.
- Create a subdomain called sounds.yoursite.com and load all your MP3s from there… etc..
Nginx has great options for directly serving static files and managing the static files caching.