Well, the error message you showed the screenshot of translates to:
Failed to download the file.
Could not successfully update to the latest version.
Please confirm that it is not write-protected file.
<Path to pso2.exe>
So I don't really know what to suggest here considering the mixed results that people have had. At most I would suggest restarting the computer to rule out certain conditions and if it doesn't update then, reinstalling the game would probably be the best bet for you too.
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