Can't add PDFs to iPad Air without losing ones already there
You don't say how you are trying to sync the PDFs or if you are using Mavericks, so I can't tell if this is helpful or not, but I have been using iBooks to sync PDFs across multiple devices with no problems.

Have a look here

Sync and save PDFs

To add PDFs to your iTunes library on your computer, drag and drop the PDF into your iTunes Book library. If you're using OS X Mavericks or later, drag and drop your PDFs into your iBooks library using iBooks for Mac.