401 Not Authorized error when trying to authenticate XML web service

[JeremyPollack]

Here's the situation :

I have the same ASP.NET 2.0 web application running on both Machine A
and Machine B. On both machines, I have Integrated Windows
Authentication turned on, and Anonymous Access turned off for the
folder that contains the webservice .ASMX file. When I hit a certain
page on Machine A, it will call the web service on Machine A, and then
it will call the same web service on Machine B. Likewise, when I hit
the same page on Machine B, it will call the web service on Machine B,
and then it will call the same web service on Machine A.

On both machines, I have an account set up for this web service to
use. The username/password for Machine A is different from the
username/password for Machine B. The machines are on different Active
Directory domains.

The websites on Machine A and Machine B use the same second-level
domain, but have different subdomains - Machine A is local.mysite.com,
Machine B is www.mysite.com.

Both Machine A and Machine B are running Windows Server 2003.

On the page that calls the webservice, I have a block of code that
looks like this :

try
{//call the webservice on Machine A
CacheMaintenance maintain = new
CacheMaintenance("local.mysite.com");
maintain.Credentials = new NetworkCredential("LocalLoginName",
"LocalPassword", "LocalDomain");
maintain.FlashTheCache();
maintain.Dispose();
}
catch (Exception exp)
{
errors = "Could not flash local cache. " +
General.UnrollException(exp) + " ";
}

try
{//call the webservice on Machine B
CacheMaintenance maintain = new
CacheMaintenance("wwww.mysite.com");
maintain.Credentials = new NetworkCredential("LiveLoginName",
"LivePassword", "LiveDomain");
maintain.FlashTheCache();
maintain.Dispose();
}
catch (Exception exp)
{
errors += "Could not flash live cache. " +
General.UnrollException(exp);
}

Machine A has no problem calling the webservice on Machine B.
Likewise, Machine B has no problem calling the webservice on Machine
A. However, when Machine A tries to call the webservice on Machine A,
or when Machine B tries to call the webservice on Machine B, I get a
"401 Not Authorized" error.

Does anybody know why I'm getting this error?

I've tried using Digest Authentication instead of Integrated Windows
Authentication, and Digest Authentication seems to work fine.
However, it seems that Digest Authentication is less secure then
Integrated Windows Authentication, thus I would like to make
Integrated Windows Authentication work.

Also, I should mention that I've only had this problem with Windows
Server 2003. I have not had this problem with Windows Server 2000.

Thanks for your help.