Ejecting a partitioned external hard drive

I recently got an 8TB external hard drive that I partitioned into two 4TB "drives". One partition is for Time Machine backups, and the other is for some storage (including my iTunes library). When I try to eject the hard drive (by ejecting one of the partitions and then choosing "eject all" when prompted), only one of the partitions ejects - the one with the backups. The Storage partition won't eject, and I get the "The disk "Storage" wasn't ejected because one or more programs may be using it" alert box (this always happens, even with no programs running). I don't want to Force Eject it because I don't want to damage any of the files. But then I can't get the Backup partition back, because it's already plugged into the computer! The only fix I've found is to turn the computer off, unplug the hard drive, then turn the computer on again. Is there a way to find out why a partition won't eject? And also, is there a way to re-find a hard drive once it's been "ejected" that doesn't include unplugging it?