Hi @Tim28068364dq01,
Sorry to hear about the issue with the Save As dialog not appearing. Could you please confirm the exact version of Illustrator you’re using? Try manually resetting the preferences by following the steps here: Reset preferences in Illustrator and then relaunch the app to see if the dialog appears again.
If the issue still persists, please confirm where exactly you're trying to save the file, locally or to a network or cloud location, and also where the original file is saved from which you're doing the Save As.
Looking forward to your update.
Abhishek