If you have not authorized ADE with your Adobe ID, you can do so by selecting "Help" → "Authorize Computer".
This error message can occur on the PC as well as in the Onleihe-App.
Even if you have authorized your device in the past, it may happen that ADE loses or no longer recognizes the ID (for example after an update). If ADE is already authorized with your Adobe ID and you still get the error message a "reset" of ADE may help: Remove the authorization by using the keyboard shortcut Ctrl + Shift + D (Windows) or Cmd + Shift + D (Mac). You can then authorize the program with "Help" → "Authorize computers" again with your ID.
It may be that already borrowed eBooks are no longer usable until the end of the loan period, as they were not correctly authorized by your ID. To test whether it works now, please borrow and download a new eBook.