Chicago Outfit Mobsters Frank and Nick Calabrese did not get made until 1983. That was because they did not want to be inducted until Angelo DiPitera convinced them to do so. I was surprised to read that because Frank embraced the Mafia lifestyle (I assumed that he was made long before that).

Joey O Masella of the Decavalcantes didn't want to be inducted either. Informant Ralph Guriano asked him and his response was that he just "didn't want it."

Another story I heard, can't verify it, is that Joseph Bonanno's brother also refused to be made. He entered the room where they were about to induct him, and reportedly saw a man there he did not like. He asked them if he was a member, and they confirmed he was. He said "well if he is a member I don't want to be made" and walked out of the room. The only reason his life was spared was because he was the brother of Joseph. But who knows if that really happened though.

According to Pistone's book,Sonny Black told him that in his early career he was doing well enough on his own and had no desire to get made.
As time went by, he realized that he didn't have the option.
Of course this is Pistone's version.