External drive HD WD 3T My Passport with Mavericks suddenly unmounts
This is a WD problem, as stated below:


  If you own a Wester Digital external hard drive, you might want to think twice before plugging it into your OS X Mavericks computer, or better yet if you haven’t upgraded, perhaps you might want to hold off on doing so for the moment. Western Digital has recently issued a statement warning customers about potential data loss on their hard drives should they attempt to connect a Western Digital external HDD to a Mac computer running OS X Mavericks. As it stands there are multiple forums threads across the internet where many Western Digital users have complained of data loss.


Source : ubergizmo

In addition, the HDD I brought back, as stated in my comment was a Western Digital disk as well.