About a week ago, I got an email from someone who works with the Aperture team at Apple. They were looking in this problem and needed some of my files to do tests.
Last week, I received an other email teling me that they were able to reproduce the issue in-house. They found that it is specific to a graphics driver update with Mavericks for those who have NVIDIA GeForce GTX 780M graphic card.
The work-around they suggested is to open the library in iPhoto and do the Red Eye fixes there. This will keep the fix once I re-open it back into Aperture.
That is not a great solution. I knew I could do that. I had tried it before. But the idea is NOT to use iPhoto for my photos. I want to do everything in Aperture, otherwise it gets to be more trouble.
They say they are still looking into the issue...