You have to be logged into an Outlook profile that has the shared mailbox as it's primary account to be able to set automatic/server-side rules for it.
You can (should) only set server-side rules for that mailbox (via that profile) so that it will fire off even with no one logged into that profile (or Outlook).
Found a decent set of (example) instructions for you here that outlines setting up an auto-responder for a shared mailbox. Here is is in a slightly edited form:
You can create automatic
email responses in Microsoft Outlook
2007 that originate from a
non-personal email account. To automatically
respond to messages, set up a shared
mailbox; and use rules in Outlook 2007
to have the mail server automatically
reply to messages.
Setting up a second Outlook profile
To set up an Outlook AutoResponse from
a shared mailbox, you need to create a
second Outlook profile that connects
only to the shared mailbox:
Click the Start menu, select Control
Panel, and double-click Mail. The
"Mail Setup" box appears.
Profiles, choose Prompt for a profile
to be used, and click Add, and type
in the name of your new profile. Click
Check Manually configure server
settings… and click Next.
Microsoft Exchange, click Next, and
enter the Microsoft Exchange server
User Name field, enter the shared
Next to finish the wizard.
To send a response with a customized
subject and message to every message:
Launch Outlook and select the profile
you created above.
Select the Inbox,
and click Tools > Rules and Alerts.
Click New Rule and click Check
messages when they arrive.
twice (don’t do anything in the "What
condition(s) do you want to check?"
Select have server reply using
a specific message, and click …a
specific message. A blank email
In the Subject and Message
fields, type the message you want to
send. Leave the To, CC, and BCC (if
showing) fields blank
Click Save and
Close to close the message window and
Select the appropriate
exclusion option (if any) and click
Name the rule (do not check the
Run this rule… checkbox.) and check
Turn on this rule.
You can now close Outlook and
re-launch it using your profile.
any message that you receive in the
shared mailbox, the server will send
an automatic reply to sender whether
or not Outlook is running on your
Hope that helps.