To have OWA Exchange 2003 prompt for a user/password

1. Start the Microsoft Management Console (MMC) IIS snap-in.
2. Right-click Default Web Site, click Properties on the shortcut menu, and
then click the Home Directory tab.
3. Under "When connecting to this resource, the content should come from",
click "A redirection to a URL".
4. In the Redirect to box, type "/exchange" (without the quotation marks).
5. Under "The client will be sent to", click "A directory below this one".
6. Stop and start the Default Web Site.

Second, I suggest you use the basic authentication. To do so:

1. Click Start, point to Programs, point to Administrative Tools, and then
click Internet Services Manager.
2. If necessary, click to expand the local computer object, and then click
to expand Web Sites.
3. Right-click Default Web Site, and then click Properties.
4. On the Directory Security tab, under Anonymous access and authentication
control, click Edit.
5. In Authentication Methods, under Authenticated access, click to select
Basic authentication. In Default domain, type your organization's domain
name.
6. Click to clear all other authentication methods.

If the issue persists, please collect the following information:

1. Please test the issue on different client with multiple user accounts.
Does the issue appear on all the situations?

2. Try to access OWA from the Exchange 2003 server directly by pass all the
proxy and firewall.

3. Try to use the URL " http://<server name>/exchange/<user name>" to
access the OWA.