SurferTim:
Try this web server with two form fields. See how it does.
Server on Arduino Ethernet fails - #27 by SurferTim - Networking, Protocols, and Devices - Arduino Forum
IDE v1.0.1 ethernet library is the only version I trust.
My friend, you - are - a - GENIUS !!!
I checked the example you pointed out for differences, and it seems that the key-difference is those two magic lines in setup():
pinMode(4,OUTPUT);
digitalWrite(4,HIGH);
that deselect the SD card peripheral that comes together with the Ethernet Shield.
Now I've been hitting the arduino with 20 concurrent requests per second for about 15 minutes and for now it is still stable as a horse!
I think those two lines should be also included in the webserver example that comes with the Arduino IDE, together with a comment explaining their importance.
Thank you so much! 
I will keep this thread update if I find something more.