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Go to admin/config/content/ckeditor and click Edit for both Advanced and Full profiles.
Open the Advanced options fieldset and add the following line to "Custom JavaScript configuration".
config.allowedContent = true;
Do this for both Advanced and Full profiles.
The solution came from the following Stackoverflow page, which also contains some other useful information:
http://stackoverflow.com/questions/15659390/ckeditor-automatically-strip...
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