How do you mean "eject an external hard disk" and how do you mean "open an external hard disk"?
Sorry, I don't know Windows backup. It's one of those programs I've never used, although I assume that Microsoft has changed it over the years.
In fact, http://blogs.msdn.com/b/b8/archive/2012/07/10/protecting-user-files-with-file-history.aspx mentions that 95% of the home computer users doesn't use it.
Maybe there's a corrupt file included in the backup? Maybe the disk is full? That's all I can think of.
And maybe it's time to switch to a better backup program.