There are many reasons to stop working your shared link.
1. Make sure the file or folder hasn't been moved, renamed or deleted.
If you move, rename or delete shared file or folder, then your Dropbox shared link may stop working. You can re-establish the link to work shared link properly. To re-establish the link, move the file or folder back to its original location, give it the original name or restore it.
2. Make sure you haven't disable the link.
If you disabled or removed the link, then your Dropbox shared link may stop working. To see the link, sign in to the Dropbox website and click 'Links' tab located at the left sidebar. If you don't see the link in your list, that means you may have removed the link. You can always create a new link to share the file or folder.
3. Make sure the link hasn't expired.
Dropbox allows you to set an expiration for a shared a link. If you are a Dropbox Pro or Dropbox for Business user, then you can set an expiration for your shared link. Check out that your link has expired or not. In that case, you can create a new link to shared it.
4. Check with your admin about your team's sharing rules.
If you are a Dropbox for Business user, your admin may have turned off the ability to share links with people outside the team. If this is the case, the shared links that you have created won't work for people outside the team unless your admin turns this permission ON.