Are you using a CMS to display these links?
I'm not sure if it helps ease the burden of updating the links, but you can tack on a versioning query to the URL, like this:
So when you upload the new file, you just change the query portion of the URL.
possible solution is to replace all the links with a short URL, and have the short URL link to the new file each time.
So, when you have a new file to upload, you just update the source link in your short URL service, but the short URL that is posted everywhere won't change.