A very good friend of mine doesn't look away most of the time when he stutters. He keeps his eyes locked with mine as long as I do the same, but not like a stare. It's exactly as if he was saying a lot of words and needs time to finish, only that he doesn't say so many words - which is actually not a bad thing because he, in contrast to some other people I know, knows how to get to the point. I'm not sure know if he likes us maintaining eye contact because even though we're such good friends, he sometimes closes his eyes in frustration or annoyance when he's having a really hard time with a particular syllable.