You need to change your PS4's DNS settings to fix this.
http://forum.square-enix.com/ffxiv/threads/311947-Unable-to-download-patch-files-20512-25008-20495-ps4#threads/311947/?page=2
The link above provides some of the settings that might work about halfway through the page. I had to do this for the last patch, and it took me a little while to find the right combination. I am sure that I will have to find a new one when Stormblood drops.
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