I finally discovered what is going on. I can't explain it, but I can compensate for it.
For, what appears to be, large files, when the image is saved in the RadImageEditor via an ajax call to save the .ImageURL path of the file, a PNG file copy of the image is created (somehow) with all annotations on it.
I don't know why a PNG copy is created, but it has the annotations. So, I can check for this file, and if it exists, then use it instead of the original file in the .ImageURL path.
Now, for smaller files, this PNG does not get created. I think this is dependent on size, but I cannot be completely sure. Maybe there's something internal to the image (GIF vs JPG, dpi, 24-bit, etc.).