Eric, as the TCP connection was reset (HTTP is built on TCP) and led to the error message you saw in the WinForms application, it is necessary for us to track down who reset the connection and then apply necessary actions.
Generally speaking, this is not an easy task as it requires both IIS and networking knowledge and it requires a lot of efforts. I can only provide you some hints here and if you like you can open a support case via http://support.microsoft.com
1. Start to capture Microsoft Network Monitor logs from both the WinForms machine and all the IIS 5 servers at the same time.
2. Reproduce this error message.
3. Stop captures and analyze the logs to locate the TCP reset packet.
4. Find out who reset the connection
That's only the first step. Once the guilty is found, it is possible to move and apply further actions.