I am the administrator of my site, so I do have full rights to do everything. I changed some menu-items (drag & drop, changed titles) and it works. Then I changed another item-title from <h4>Abonnements</h4> to "Abonnements", so without these senseless <h4> tags. After that the message (in German) "You don´t have the rights to access this page" appears, when I click into the settings of Admin Menu Editor.
Everything else in my Adminarea works. What is wrong there? And no: I did not change userroles or role-settings within Admin Menu Editor at all.
PS: Many people seem to have the same problem, but without any fix since at least 7 months!? http://wordpress.org/support/topic/plugin-admin-menu-editor-you-do-not-have-sufficient-permissions-to-access-this-page?replies=7
The advice in this thread does not work at all. There need to be a real fix of this issue.