How can I turn off the ability to "Work Offline"?

Here is the Situation: In our mainframe room, we have 8
people using 2 machines setup identically. These are 2
sets or Day and Night crews. These 2 machines are logged
in to our Local Domain with the same user ID so that
there is no confusion with password lock-outs since all
of the 8 users are classified as "USERS" and no admin
rights are available to them. Keeps me from getting a
call at 2 am.

Here is the Problem: Outlook 2003 uses "Profiles" to keep
track of each persons email. It downloads a "Local Copy"
for each user when they log into the server depending on
if they type in their password correctly. If they don't,
OR sometimes it doesn't ask for one, it shows
the "Offline" in the right-hand corner of the status bar.
The messages that were there since the last time they
logged in are still viewable, (Inbox, Deleted, Sent...),
since they are working in "Offline" mode.  ***  If User#7
wants to find out what User#1 has written to Boss#3, all
he has to do is choose User#1's profile and he can view
anything that was written from the beginning to the last
time User#1 logged on.

How can I turn off the ability to "Work Offline"?