Download file one time only for auth user (Suggestion needed)
Please use the modules tag if you're looking for a module hosted at Drupal.org.

There exist a module named Deep Link.  With 13 installs and no full release in sight, I wouldn't have high hopes for the usefulness of this, but the project page says:


  Deep link module allows the direct access to a specific item of content under certain circumstances and limitations. Such as one-off or time-limited deeplinks.


There is also Expiring Private File Link.

It says:


  This module was created when the need arose to offer a downloadable file to users of a site, without revealing the actual URL of the file itself. It also allows through the permissions system a method of allowing the file to only be available for download to registered users. If enabled, anonymous users will see the same dynamic link as registered users, but when they click on it they are presented with a login dialog informing them they must register to have access to the file.


This is a sandbox for Drupal 7, so its usefulness is even more questionable, but you may still want to check it out.