Refreshing a web-page hangs after few times
The code you have that says readString += c has to allocate a whole new string whenever it runs out of space for more characters. All those allocations are filling up memory. 

Instead of the String class, use a single C character array, e.g.

char s[128];

that is big enough for whatever you put in it.

If it helps, I wrote a simple arduino web server for my own project, and if you look at the code here that may give you ideas for how to implement this.