I found this thread only today when I plugged in a Seagate 3TB external USB3 drive, got it going with Time Machine, and was then amazed to see that when the machine slept and woke, the drive was disconnected. It would not remount automatically, even though powered on, and in place of the proper icons were those messages about the drives (two partitions) not being properly disconnected.
I skipped ahead about two years to the last page of the thread, found the reference to Jettison, paid the monumental price of US$4.95, and installed it. It takes care of the disconnects, and it keeps Time Machine running properly. It does not, however, seem to prevent those nasty "disk not ejected properly" messages when the machine crashes.
Now it's my belief that all, repeat all, Jettison is doing is a small set of tasks that the OS itself should be performing itself -- checking to see if there's data in cache waiting to be written to a removable device, making sure that it's written, dismounting the device, and then issuing the sleep command. Windows has done this for decades, and it borders on incredible that such an apparent bug should remain in Apple's latest iteration of OS X. If Apple refuses even to acknowledge the problem after two years spanning 3 upgrades of the OS, then that is reprehensible.