Need to ask some questions:
1. What exact Mac model do you have? ***Macbook Air 7.2
2. What exact Mac OS are you using? ***10.12.6
3. Have you ever done an disk cleanup/maintenance/repairs, from a software perspective? By that I mean have you ever run any disk-related software to help with those tasks? There are some excellent products available (both free and commercial) that can help you with that. ***No, The external disc a week old and has only been used with this computer. All I want is the password requirement to stop.
4. This is critical: are you making backups to an external device? If you are, what software are you using for that? And is your external drive used for such backups? Used Time Machine to do a backup, but turned it off in hopes it would help. No change. External disc is NOT encrypted.
5. What model/brand is your external drive? ***G Drive Mobile
6. Do you remember the last "activity" involving that drive before the issue started?