DL links appearing multiple times on live site

In the last few days I have updated a number of documents for the staff web site that were due to expire soon. Now, we have both the 'old' and the 'new' DL links appearing on the web page, when obviously only the 'new' ones should be published.

Of course, the links in both versions point to exactly the same document (the permanent URL) but we don't want to see multiple links to the same document. Why is this happening and would a purge and update on the staff site resolve this?