time machine couldnt back up My Passport Air

The file system on most USB external HDD's is some form of FAT or NTFS and may not be supported by the time machine software. I ran into a similar compatibility issue a while back using a time machine style backup software (back in time) on a linux system. These style systems rely heavily on symbolic links to do the magic they do. I will never again make the mistake of using a filesystem not designed for solid reliable back up use. I have since used gparted to repartition that particular device and put an EXT filesystem on it for future use. You may be able to work around your issue by taking a similar approach. You do give up portability to non linux systems with such an approach. Good luck with that project.