I had the same problem couple weeks ago and no one could help not even SE support but this is what I did to get it working again and haven't had any problems since then.

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Settings > Application Saved Data Management > Saved Data in System Storage

First back a back up of you saved data by selecting "Copy to USB Storage Device" and make back up for your XIV folder (this also allows you to transfer your settings to a different PS4 also)

Then go to "delete" and select your XIV save folder and delete the "system data" file
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Here the thread I originally posted it in
http://forum.square-enix.com/ffxiv/t...ing-logging-in