Core Search Module in Drupal 7.14 and Hidden Fields
This behavior is the correct behavior for Drupal search out of the box. The default search module only indexes fields that are not hidden in the default display view mode as Clive suggested on 8/10. This prevents anonymous users from searching and returning results hidden from their view, yet exposed via search. The exact mechanics of it vary in application from D6 to D7 but both use a concept of search index version of the node which is used to create the indexes in the database.  You can alter what the search indexes by modifying this view of the node.

In D6 you would be able to get around this by altering the node_api for the search index as shown here: http://drupalib.interoperating.info/node/246.

In D7 you can choose to enable fields to be indexed that are normally hidden in the default view.  Edit the content type and go to the manage display tab of that edit screen. Below the fields portion of that edit screen is a collapsed portion of the page for custom display settings.  Open this section and select the Search Index view mode. This will now allow you to alter the fields used to index the node.  Keep in mind the relevant results portion of the node will be blank in search results unless you also alter the search result view mode.  In this way you can have different results indexed than the visible fields in other node view modes.

You may also choose to implement the search api module, or make this field visible to the world in your default view mode and handle obscuring it through css or the theme layer.