Why would you want a shout to stay in a shoutbox longer if you're in a conversation with someone?
So that you can :
1) Pick out important info if you are trying to join the conversation
2) View useful history, instead of nonsense
3) Not have a laggy forum, because shoutbox history gives the forums lag. With the like button, we wouldn't have to clear the shoutbox as much.
4) Help the moderators. With less history, mods can easily see who's said what.
Here's an example of how hideous it would look.
That looks tacky. So maybe if we make the image smaller, and the colours more suitable for this theme.