Platform: Windows
Type of Internet Connection: Cable
Internet Connection Speed: 100MBps
Date & Time: April 2, 2016
Frequency: Always

Steps:

After moving from console to PC, I noticed that I can't download any wallpapers from PlayOnline anymore (greeting cards also cannot be downloaded).
Since they are mostly related to the game, and FFXI being the only game that uses POL, I would consider this a bug with the game (since there is not a specific PlayOnline bug section).

I can confirm that the downloads have worked perfectly at around middle February on Xbox 360 and earlier in 2015 on PlayStation 2.
Now trying to download any of those extras just shows *** instead of "Downloading wallpaper x/y" or "Downloading greeting card x/y".

I do not know if these downloads stopped working on PC before console support closed.