I saw Stritch in ALNM, and she went up on her song a few times. It was kind of embarrassing, and I felt kind of bad for her. She did recover eventually, but it wasn't like she was improvising in a smooth manner. Ultimately, she did put it over after a few of these interruptions, but I felt at the time that she should have taken up the offer to use an earpiece. Otherwise, she was quite good in the role.
Barbra Streisand uses teleprompters in her live shows, btw. I think nearly all the patter is there as well. Although there was some shtick with names and questions sent to her at her Brooklyn concert where she was apparently off-prompter. She said of one note's sender that she received, "Sierra Boggess. Sierra Boggess! What a name!" I kid you not. :)