When applying covers from Inbox to a max ability character (e.g. 5,5,3 character) the cover will be added to the saved coves. Unfortunately if you have multiple covers to save using the "Save Cover" button won't add the covers from the Inbox to the saved covers of that character (e.g. if you have 5 saved covers you could click the "Save Cover" button 10+ times and none of the covers will be added to saved covers).
To add to this, it seems to be an issue if you have an ascended cover in your queue. Once you do something with the ascended cover it works fine.