It looks to me like there is a problem in the Ethernet library when the RX buffer is not being read quickly enough. For example the RX buffer may be being overwritten by another GET arriving later.
...or a GET that is waiting in another socket times out because the previous (active) GET is not processed fast enough. I found the faster the code, the better the responses.
I used three independent instances of Webinject to load up ST's form sketch with 1000's of simple GETs and everything worked ok. So the ethernet library can logically handle more than one socket connected at the same time.
As it does here.
I also checked the max connections per server registry key
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Internet Explorer\MAIN\FeatureControl\FEATURE_MAXCONNECTIONSPERSERVER
and it is set to 2
This is why I used three computers for my test instead of multiple instances in the same computer.
Maybe you can talk zoomkat into posting his auto-reload code for you, and you can test with it using web browsers for the test. That way you can see the difference between "connecting" and "connected". Maybe WebInject requests time out too quickly?
edit: When I tested this, I read the GET request (rx buffer) as fast as it would read it. I put the delays in the response (tx buffer) after the header send. A web browser will wait much longer if it has received something from the server.