I have been having the same problem with my backup drive. I originally thought it was associated with Sleep/Wake. I now, however think that something else is the cause.
I read through most of the posting in this thread, and tried the suggested solutions. I changed my preferences to never sleep; I then also used Caffeine to prevent sleep; I tried the “Swiss Fix”, I even tried the OnyX suggestion; and I went so far as to erase and reformat my backup drive, but nothing helped.
Anytime I leave my back drive mounted for more than one backup (automatic or manual) Time Machine will begin the next backup (Preparing Backup), and then the disk will eject after several minutes of this Preparing backup mode.
I have now reached the point that I doing manual backups as needed, eject the disk myself, and remount the next time I want to backup.
I’m not sure what to try next. I’m thinking it is either a bad external hard drive or a problem with my system software. (This may or may not be related, but I have noticed at times I have applications that are running, but do not show up in the dock. I notice this when emptying the trash, and I’m told that the file is in use. Pressing option-command-esc shows the running applications. I do a Force Quit, and all is fine.) I really don’t want to reinstall Mavericks, and do a restore of my applications and documents, nor do I want to invest in a new drive, but I might be out of options.
Any other suggestions?