Dear 01bex_multi,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, it seems that you are trying to save the Unsaved Document (.asd file) with "Save As" option, however, no error prompts and file does not get saved in Windows device.
If the understanding above is right, considering that it is an unsaved document that contains important data and you have tried both save as option in Word, to avoid data loss, we'd sincerely recommend you contact your Microsoft 365 administrator if you are not the admin of the organization, follow steps in this article to contact Online Support. The support team over there has higher permission than us, they can remotely help check the situation on your side, involve more resource to collect logs and help you restore the unsaved file safely. This would be a more efficient way in handling this case for you.
For reference: How do I find my Microsoft 365 admin?
We'd also recommend you navigate to the folder and copy and paste the unsaved file in another location, use another device/ local profile to open the .asd file and try saving the file as .docx file to check the outcome to avoid data loss.

For your reference: How to recover unsaved Word documents - Office | Microsoft Learn
Create a local user or administrator account in Windows - Microsoft Support
Thanks for your understanding and cooperation! Have a good day.
Sincerely,
Rhoda | Microsoft Community Moderator