A doclink comprises two key components, the replicaid of the database holding the document and the DocumentUNID of the document itself. When a document is moved from one database to another (such as the case with archiving) both the replicaid and the DocumentUNID will change. As a result, the doclink is never going to be able to work.
Based upon the description you have given I would suggest you may need to build some additional logic into the archive process to modify the doclinks at that time (and/or save the original DocumentUNID as part of the archive so an agent could rematch the documents).