Joomla’s editor will strip out any HTML attributes it doesn’t know, which includes usemap. To add that or another unknown image attribute to the allowed list, open
/plugins/editors/tinymce/tinymce.php
and find if ($advimg) Add |usemap to the collection of |-separated attributes after $elements

We also set the editor on Joomla to “extended” functionality, but I don’t know whether that was necessary after editing TinyMCE.