CKEditor doesn't work with multi field (Drupal 7)

This is the Drupal 7 case for the problem defined and discussed here: http://drupal.org/node/953210

I created this separate issue per the module maintainer here: http://drupal.org/node/953210#comment-6267318

From the other case:

CKEditor doesn't work with CCK multifields: When you click on add another item the editor disappear from the 2 textareas first items and their content is erased.