Guess no one is looking at this topic.
Some updates: I was wrong. It doesn't do a time machine update while it is asleep.
I moved the external HD from the USB connection on the back of the iMac to another one. Didn't make much difference. If I'm on the computer for a while the time machine does back up the Macintosh HD every hour and the backups look good.
Disk Utility didn't find a problem with the external disk. This only started happening about the time the last update to ElCapital was installed (10.11.3). But, if it were a problem with the update others would be posting about it. So far I don't see any others with this problem. The Seagate 2TB external drive has it's own power supply, so it shouldn't be trying to take power from the iMac USB.
I tried setting the Energy Saver System Preference to "Enable Power Nap" and it did do backups while asleep, but then I work the computer, I had to log back in as a user. I still saw a few of these messages in that mode. The only box checked right now is Wake for Network Access. Not sure that is necessary, but it is the default setting.
Do I have to eject the external drive every time I leave the iMac? That would probably solve the problem. But then I think I'd have to unplug it from the USB and then replug it for it to be seen again when I awaken the iMac from sleep. I hate to do that. Maybe I could cycle the power supply on the external drive so the iMac could remount it?
I've looked at the logs, but can't see anything that jumps out and I don't know how to read them any way. I'd be pleased to take a screen shot of a log, if it would help identify what is happening here. May not be a serious problem. But in my five years experience with the Apple world on a MBP 15" early 2011 and on this iMac 27" 5K I have not seen this problem until the past few weeks.
Hoping someone with more experience can give me a suggestion. Am I fighting with windmills here?
Thanks,
Veehb