WiFi shield unresponsive after a while

Here are the pins reserved by the shield, as noted in my header files.
You may have to adjust the numbers for your DUE

#include <SPI.h>
#include <WiFi.h>
#include <SD.h>

/* Pins Occupied by WiFi shield
WiFi
  SPI occupies UNO pins 
  10 - SS, shield select 
  11 - MOSI, Master Out Slave In 
  12 - MISO, Master In Slave Out
  13 - SCK, Serial Clock
  
SD card 
  4 - SS, Slave Select*/

I don't yet know enough about the electrical stuff to say
which pins MUST be kept clear. Keeping all of the clear
works for me, as they say.

Network protocols I do know about. I think I said elsewhere,
the example web server is not a great place to start learning.
The example code does not conform fully with the HTTP protocol
which means you are in unknown territory.

I am attempting to write a conformant web server but I am not there yet.