I use several different programs to access the same file in the Dropbox on Windows, iOS and OS X. All those different apps/programs update this file. After some days/weeks the link I use in the iOS App to the file changes and the App does not work anymore with this file. When, under which circumstances does Dropbox changes the link of a file?
Whenever you change the path of the file on the device you are syncing from,
the public URL changes to reflect the change in path.
[I can only confirm this for Windows based devices.]