Thank you for the response.

There are actually two different limits, inbound and outbound, on Windows XP. The above error message, I believe, is related to the outbound limit that Microsoft added primarily to reduce the rate at which viruses/worms spread. More information may be found here:
Microsoft Article Event ID 4226

I believe that the original poster in the linked forum thread was intending to use Windows XP to run Oracle Database (Windows XP acting as the server). There is a 10 connection inbound limit for Windows XP Professional and a 5 connection inbound limit for Windows XP Home. More information may be found here:
http://support.microsoft.com/kb/314882

The corresponding error that will be returned to the remote computer when the inbound limit is reached is “No more connections can be made to this remote computer at this time because there are already as many connections as the computer can accept.”

Additional information may be found here: http://support.microsoft.com/kb/328459 Quoting:

This problem occurs when a computer reaches the maximum number of host connections that are allowed. In this case, when a NULL session connection is generated in the Microsoft Windows 2000 client, this NULL session connection is counted as one session on the Microsoft Windows XP-based server. Therefore, the error messages occur that are mentioned in this “Symptom” section, even if the number of connections to computers do not exceed the limit.

In addition, when multiple NULL sessions are generated from a single Windows 2000 client computer, the multiple NULL sessions are counted as multiple sessions. However, a NULL session appears as a single session when you run the net session command. In this case, when the RestrictAnonymous registry entry is set, and the NULL session connection is rejected, this symptom still occurs.

Notes

For Windows XP Professional-based computers, the maximum number of concurrent network connections that are allowed is 10. This limit includes all transfer and all resource share protocols. For Windows XP Home Edition-based computers, the maximum number of concurrent network connections that are allowed is 5. This limit is the number of sessions that can be hosted at the same time from other computers. Therefore, we cannot use the administrative tool usage to connect to the system from a remote computer.

When multiple NULL sessions are connected from a single computer, each one of them is counted.

Only one IPC$ can be checked by using the net session command. For example, when a single Windows 2000-based computer tries to use multiple IPC$ sessions, only one single IPC$ session can be used at a time.

RestrictAnonymous is not valid for this resolution.

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The bullet point item in my blog article is a bit confusing/inaccurate because it combines an outbound error message with an in-bound limit specification. I am having trouble locating the exact outbound limit to determine if it is the number of connection attempts per second, or if it is the absolute number of half-open connection attempts.