Windows Authentication Problem with Tomcat

This problem has been driving me crazy. I'm sure there's a simple
solution, but I haven't been able to find it. The consultant set it
all up, so forgive me if I don't understand exactly how it all works.

We purchased a 3rd party application that runs an embedded Tomcat
server. This runs a web application for reporting -- all jsp
scripts. It uses JCIFS as a connection mechanism. This writes and
reads to a SQL Server 2005 database. Everything is set up in Active
Directory. IIS 6.0 with an application pool configured. Somehow the
application pool and tomcat work together. I'm still not clear on that
part.

Windows 2003 R2 SP1. IIS is configured with Windows Integrated
authentication. Tomcat is configured to use the NT Domain as well.
Users are domain users and have the necessary permission to access all
resources -- SQL, website, app pool.

The problem:

A user can access the reporting website using the URL http://servername:portnumber.
The user is automatically authenticated and can get to everything she
needs. HOWEVER, if another user attempts to log in to the reporting
website, the user is prompted for a username and password,, but the
credentials do not work. This same user could log on later when the
first user logs off. Sometimes it all works fine. Other times, this
problem happens.

Does anyone have any ideas about how to resolve this?

Any help is very appreciated.
Beth Stover