First of all, you're using the String class, so sooner or later your code will crash. If you plan to run your sketch for more than the first few requests, get rid of that class and work with character arrays only.
The next problem and probably the cause of your slow downs is that you only read the header of the HTTP request and then you send the whole page, ignoring the rest of the request.
Fix these two issues and post again if the problem still occurs.