Listing Visibility – private- function not working

Hello and Happy New Year!

When I create a new listing for my properties, I would like to have the function “listing visibility” to work on Private, but this function is not working. Instead I have had to use the “protect by password” but that still shows up on my listings. Ex: http://reislux.com/listings/page/3/ and following it to http://reislux.com/listings/moradia-v3-para-venda-em-santarem-com-piscina-horta-e-pomar-casa-de-hospedes/.
What am I doing wrong?
I need this function for properties where the real-estate contract is still not signed by both parties (in case of a divorse, for example) or for very exclusive pre-listings for investors.
Thanks for your help. Sonia

The page I need help with: [log in to see the link]