Found this solution from a forum post way back, worked for me (first step).

Some things that can solve the problem:
1. Uncheck the case "Read Only" in the Properties of your Square-Enix and My Games/Final Fantasy XIV: ARR folders
2. Run as administrator
3. Use compatiblity mode to XP.

That worked for me last time I had this problem. But that's still a shame we have to go through this to update every time, and since the beginning of beta tests.