Login to plesk, select the domain, click web directories. Here, select the the protection tab and click remove protection if enabled.
If that does not work, try resetting the FTP password from the setup section.
If the site still asks for login, connect using remote desktop, run cmd and then enter the commands:
cd %plesk_bin%
websrvmng --update-anon-password --domain-name=
This can also be run for all domains in one go with the command
websrvmng --update-anon-passwords-all