Reasons I can think of:
1. Drive is full. Check and free space, google that if not sure how.
2. You need write permissions to the directory. Right-click on Documents\My Games and make sure it and all sub-directories have write permissions.
3. Use a user with admin and run the game as an admin.
4. The file may be corrupt. Go to Documents\My Games\Final Fantasy XIV - A Realm Reborn, find your CHAR folder and copy/backup all the setting files. Then delete them! It'll reset your settings, but it might allow them to save.
5. Most crazy thing - does the above directory exist? If it doesn't, it would certainly be struggling to save to it. This happened to me with the screenshot folder. Needed to exist first.

I know that One Drive causes people lots of issues, such as constantly restoring settings after the game changes them and frustratingly erasing settings or new patch updates, so I'd personally keep well away from One Drive as long as I am an FFXIV player.