Hello,
I've got this problem once ... and found out why (at least one good reason). Here it is. It requires some Unix trivia.
-You can't "unmount a volume" if some process has an opened "handle" on it.
Then, you got to figure out "who" has a lock on it. There are sysadmin tool to do that (fuser), but it's complex. In the case of a Workstation operation - like most of the Macs are, you can try closing all your applications preventively and exit from your account (Ctlr-Cmd-Q), or reboot.
In the case I've identified, it was Time Machine Preferences Pane that was dead, but dead to a point it became a "zombie" process. It means that the process is dead, but the kernel of your Unix machine has not been told it was fully "dead". It's really gone, but the process is still listed as "alive". Hence, the "zombie" name.
I've saved the list of my processes in text file the last time it happened:
501 1063 171 0 0:00.00 ?? 0:00.00 (System Preferenc)
A zombie process is shown in parenthesis. There is not much option - on the system administrator side - to update the kernel process list, but a gentle reboot.
So: nicely close by hand all you applications using the application switcher: Hold Command key down and tap on the Tab key. For each app, tap Q. If the Finder is responsive (it may have been locked up trying to unmount that TM volume) try Restart, or press the PowerKey if your machine has one reachable (or Command-Eject for 1").
---> Now: Why did TM got hosed like that? First, I don't know and have reported it.
In my case, I've setup my Mac to not login onto my account by default.
If I plug my Fw TM drive BEFORE logging in, then TM goes into an endless loop telling "Preparing" ... but under the hood TM is already "zombified".
So: Always plug your TM drive once you're logged in ... until further notice.
If this description doesn't match your case, anyways, my description above is always true: You can't unmount a Volume if some process has a lock on it.
Hoping this helps.
Thierry