This is the original image, a small section of a large image, scanned from a negative.  

This image was chosen to include highlights, shadow detail, and a variety of colors.  This image contains no saturated blue, so we expect it to fare pretty well when converted to CMYK, or will it ...

color settings

(click on the image to open it in a new window)

This is the same image, converted to CMYK, and then back again.  Can you see the difference?

Here I've repeated the RGB->CMYK->RGB conversion 10 times.  Now can you see the difference?

Here's a composite view of all three images, each occupying a vertical band 1/3 the width of the image.  

Can you see where one image begins and the next ends?

 

 

A histogram illustrating how much the red channel of the image changes with a single conversion from RGB to CMYK and back again.  It was calculated by using Image>Calculations... to calculate the difference in the red channel before and after the conversion.

The average pixel changed by less than one.  Not much in the scheme of things.

 

The same histogram, calculated the same way, only we have converted the image back and forth between RGB and CMYK 10 times.

The average pixel changed by about 2.  Significant, yes, but still not enough to visibly degrade the image, and this is way more than you or I would normally convert the image in the normal course of events.