I've had this same recurring problem since way back in the Illustrator V10 days! It's clearly a bug and I can't believe it hasn't been fixed!
My eyedropper works sometimes, then it doesn't. Here is a classic example: I am trying to colour the text the same colour as the yellow graphic. So I select the text and use the eye drop tool and you can clearly see that the yellow colour shows up on my colour-picker but not on the text I'm trying to colour.
My settings are all correct (see grab)
At times, a workaround is for me to deselect the eye dropper preferences boxes and then try - it usually works, but sometimes it doesn't (like now).