In case your LiveAgent is very slow or not loading at all, one of the possible reasons might be your server setup - check if your server uses Cloudflare. If it does, Cloudflare is messing response data and also works with some kind of cache because of which the LiveAgent simply cannot work.
To fix the issue, create an exception for LiveAgent so Cloudflare is not used for it.
How to find out if Cloudflare is used
Either ask your server hosting support or try checking server requests with Google Chrome Developer tools, or Firebug for Firefox. The request header contains a server header - check it. If it says cloudflare-nginx. If it does, Cloudflare is used... Here is an example of how the request might look like:
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Cache-Control:no-store, no-cache, must-revalidate, post-check=0, pre-check=0
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CF-RAY:119513d6de84072b-AMS
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Connection:keep-alive
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Content-Encoding:gzip
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Content-Type:text/html
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Date:Fri, 11 Apr 2014 06:20:21 GMT
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Expires:26 Jun 1997 05:00:00 GMT
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Pragma:no-cache
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Server:cloudflare-nginx
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Transfer-Encoding:chunked
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Vary:Accept-Encoding
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X-Powered-By:
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X-Powered-By-Plesk: