Has the app you are using requested access to the whole SD card?
I can't remember the technical name, but as of Android 5 apps have to make a specific request to gain write access to the full card (as opposed to a little sandboxes area of its own), not just have the permission granted as they used to have before 4.4. Now I don't have a more recent android device with an SD slot so can't confirm that it's not changed again since then, but that's the first thing that occurs to me.