New
#11
There are several potentially relevant & effective suggestions already mentioned above (many of which serve to effectively close open handles on the external drive). If none of those work, it is very likely that Windows still has open handles on the external drive. If you are a bit technically oriented, these open handles can usually be detected using Sysinternals Process Explorer. See this post in another recent thread for more info regarding how to use.
This is usually my first (and only/last necessary) investigative step when 'Safely Remove Hardware and Eject Media' will not work, as it nearly always removes the guesswork. [I should mention that it is easier for me to do this quickly, as I always have Process Explorer running anyway, but starting Process Explorer to solve the problem only takes about 20-30 seconds.] Once you see what handles are still open for the external drive, you can make a better informed decision about what files/programs may need to be closed to close the open handles, or if you can 'safely' go ahead and unplug the external drive in spite of the Windows warning (see discussion in other post already mentioned).
As implied by MeAndMyComputer in the immediately preceding post, the 'safest' (but more annoying) approach for avoiding data loss is probably to shut down the PC before removing the USB drive. But in my personal experience I have rarely had to resort to shutting down, as I can nearly always figure out a solution with Process Explorer.