Map an LDAP user into Nexus 3, and log in as this user.
Change the user's LDAP password. Don't log out of Nexus, instead restart the web browser. Then wait 5 minutes for the cache entry to expire, and try the login again.
It won't work with the new password, you still need to use the old password. Users have reported waiting over 24 hours, and still the old password works. It is necessary to manually clear out the LDAP cache in Nexus 3 to fix this.
Note that if you do log out of the UI the cache entry is cleared, and the new password will work the next time.