ESP8266 Web Server stops responding after a random period of time.

I am using this library to set-up a simple web-server with a static IP address. Everything works fine and the server is able to handle request from multiple devices.

After a random period of time (a couple of hours) the web-server becomes unresponsive. At the same time I am able to ping the ESP8266 and receive replies back, so the device is alive and well.

Is there anything I should be aware of based on how connections are handled ?
Is the server ok with handling mobile devices as clients ?