How to edit markup on existing pages using version 4 of the CKeditor library in Drupal 6?
CKEditor Version 4.x is known to have 'some' issues, at least when used in DRupal. The issue you described in the question here is probably one of them. And it doesn't matter if you use the CKEditor 'module', or the WYSIWYG 'module' (in combination with the CKEditor 'JS library'). Because for both modules these issues exist.

In my experience, going back to CKEditor 3.6.x version (or never upgrading from 3.x to 4.x) has always been the best "compromise", since in the 3.x versions these issues seem to not exist.