Hi @capmoe,
The admin prompt is required to update the /etc/hosts file. Editing the /etc/hosts file is what allows you to access Local sites at URLs such as example-site.local. This prompt should only show when you add sites, delete sites, change site domains, or sync multi-site domains.
If you’re sure you’re entering the right password, there may be a permissions issue with the /etc/hosts file, or it may somehow be locked.
To save you the trouble of tracking down why you’re unable to edit the hosts file, I recommend upgrading to Local 5.2.1 or newer which has a new “localhost” routing mode. Once you switch to the “localhost” routing mode by going to Preferences » Advanced, you should no longer get the admin prompts to edit the hosts file.