The list in the 'Open My Recent' documents area are just a list of shortcuts.
If the files are moved after the program is closed the 'Recent' list will not work correctly.
In OS X you can search using the following methods:
The Finder toolbar also includes a search field. This field searches the files and folders on your Mac and disks that are currently connected. Click the field and begin typing terms you are looking for. As you type, items named with these terms or that contain these terms appear.
You can narrow your search further by selecting a search token for each term. Search tokens such as "Name matches" appear as you enter a term. Click the token you want to attach it to that term.
To change a token type, click the token and select an option from the menu that appears.
You can also select Search criteria to narrow your search from the menus that appear at the top of the search window, such as Name, Kind, or Contents.
To combine search criteria, click the Add Criteria button (+) to the right of the current criteria. Combine multiple search criteria to narrow your search further.
If this is a search you use often, you can save the search as a Smart Folder.
Opening this folder shows you the latest results that match these search terms.