can't sync not enough storage

Hi,

I'm trying to sync new videos to my iPad Air (also, I have the same problem with my iPod Touch bought new August 2014), and when I get to a certain point in the sync it says "cannot be synched because there is not enough free storage", and usually it's a small amount like 1.5 GB needed when the space allocation bar at the bottom of the window clearly shows over 8 GB free.

Also, when I try to sync and this problem shows up the Apps section of the allocation bar fluctuates between 9.8 GB and 11.01 GB for no apparent reason.

I have read the other discussions on here with similar problems, and the consensus seems to be remove everything and resync. The problem I have with that is that after I got one of those messages I tried to sync one item at a time it worked once before giving me the problem again.

Is this just a dumb glitch with the new iOSes? Would like a straight answer, don't give me a link to a non-existent article and don't tell me to take off everything, I have serious doubts that that will fix everything. Plus, Ihave a lot of local data that is impossible to back up.