Sorry to be so blunt but..
Simply put..he has to tell her. By not telling her he is in effect having an affair with everyone else when you look at the premise of exclusivity that he has passively lead her to believe. This will not get any easier on her the longer he waits..it will get worse. I will be so bold as to call this straight out selfish in that he is putting his needs ahead of hers. That is not polyamory. Put yourself in her place and force the issue. She deserves to know.