I am running the latest version of El Capital, 10.11.3. I only started to see these messages after this last update to El Capitan. I have seen no data loss and when the iMac wakes up, Time Machine jumps in and does the next scheduled update. So, I really can't see that it is hurting anything, but the messages are annoying. I don't like to ignore message that warn me that my external disk was not ejected properly. Nothing has changed in the driver on the external disk, so OS X must have changed. I've tried this on both a native port and on USB extender, with a power supply. Doesn't seem to matter.
I've also had trouble syncing my Fitbit Charge to the iMac. The iMac has a sync dongle plugged into a USB port and the Fitbit software running in El Capitan can't find the dongle. Sometimes after many tries it sees it. Never had this problem before the latest update to El Capital. The Fitbit website notes that there have been some problems since the last update to the Apple OS X and that "Apple is working on the problem". I suspect there is a bug (or several) in the USB driver that was introduced with the last update. But, the posts here go way back before this latest update, so maybe there has been a problem in the USB driver going back a few years?
I find it interesting that the Apple Support Site is pretty silent on this issue.
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OK, after writing the above (iMac was asleep all night) I went to Time Machine and saw that it had not run since last night. Then I noticed that the Seagate external disk was not connected. I unplugged the USB cable and then plugged it back in. It didn't mount. So, I moved it to a different USB port on the iMac and then it connected and now Time Machine sees it and is doing a backup.
This is a most frustrating problem!