Nevertheless I followed ADSR's suggestion and disabled the drive in Spotlight preferences. I will advise if that makes any differences.
I'm going to look into that as well. Merci!
I trashed the contents of a flash drive once by not ejecting it, that won't happen again!!!
I did that also, by pulling it out too soon. Then I notice the light still flashing after the icon disappeared. From that time on, I have waited longer before pulling it out.
... I ... disabled the drive in Spotlight preferences.
Ok, how did you do that? 
I don't see anything in Spotlight preferences to disable a removable drive.
Try disabling the drive in spotlight preferences
Gregg, it would have to be mounted for the option to appear. It's in the Privacy settings for Spotlight - you just click the "+" button and then add the flash drive. I just did it for one of mine.
What am I missing here. Aren't the above contradictory? Or is "adding" the flash drive the same as disabling it? This hurts my brain! Everyday when it's quitting time at work, I have to click on the Start button!!!
I did close the Spotlight Preferences and insert the flash drive, then reopen SP. I did look in the Privacy settings.