As a prompter operator, what happened today represents an absolute, worst-case scenario playing out. According to his blog post: "I skipped over the Exec VP’s intro line and then the teleprompter got lost."
Normally when someone goes completely off the rails like that I just stop. If nothing else, I try to find a good point for them to pick back up again, but that's not always possible. Sometimes they've gone so far that you can't find them again.
This situation is a wonderful example of why the talent should show up to the rehearsal, and why rehearsals are such a critical aspect of live shows. Dialogs between people onstage like this aren't common when using a prompter, for exactly this reason. People will screw up and read the wrong person's line, or ad-lib, and it messes both people up. I try to color-code each person's lines if I can but again, not always possible.
I can handle ad-libs. I can handle changing up a turn of phrase or riffing around with the script. But if you go way outside of it, you can't expect me to keep up with you.