Web servers and web hosting companies are putting in rules to limit and / or eliminate denial of service attacks.
One such rule is to limit the number of connections in a short period of time from any given IP address.
As a web page loads and it has to load each css and js file, each of these may cause an additional connection to the web server. It doesn't take long to break the firewall rules and have your connections limited.
One solution to this is to combine CSS files when possible and to combine JS files when possible.