I had this issue with an iPad Air 2 in a spectacular fashion.
iTunes showed 64 GB or so free. iPad kept running out of space, showing only a few hundred MB free. WTH?
Had to do a full backup and then a hard reset/wipe of the iPad and a restore. When I was done, I had 83.8 GB free. WTH?
Looking at the storage, the bulk of the difference seems to have been in the Videos, Music, and Newsstand Apps. As close as I can figure, if you do something like an iOS update while you've got a rental movie, or perhaps something else, it loses track of things and keeps that memory walled off. Maybe some other stuff as well. The Newsstand apps it wiped the issues and didn't restore from backup, which is a pain in the a** as well.
11-09-2015 04:50 PM