UPDATE: Checked her Group Options, clicked the "Current Group" button. All the options where clear, with Autosplit Coin and Autolock Encounters checked. I modified the "Looting Method" to be "Free for all" and the "Auto Loot Mode" to be "none" and hit Apply. Now she is once again looting her shinies! I don't remember changing her loot options when she initially started not being able to loot them, but its working now so thanks guys! I have one character, Wazephyr on Skyfire server, who does not receive a shiny when she clicks on one. I see the "collection" casting bar, it completes, but the shiny doesn't not appear in her inventory. This happens on normal "white" shinies and the special ones from her Solstice earring. She is level 121 now and it just started happening. I don't think it coincided with her levelling. All my other characters (who are on Halls of Fate server) collect their shines with no issue.
Do you get a loot popup window to loot the shiny? Is it possible you are set to auto decline on loot options? [I would try changing your loot options]
Make sure your overflow is empty, check your bag settings, switch at least one that has room to default settings and try again
