Do barbarians cease to rage once they become unconcious ? My take is that they do, because the can voluntarily choose to do so normally - therefore the rage must have some component of concious activity.
Your asking this due to the old "stop rage" = dead barbarian ?
I hate the insta-stop rage. Our DM enforces something like this. The last enemy falls and suddenly all the Rage or Adrenaline goes away. Barbarian drops. I think DMs should at least give 1 more round "cooling off". That should be enough for the party cleric to save the barbarian... even if he is knocked out on the floor. IMHO. Adrenaline doesn't stop like that... even unconcious.
Ruling that rage ends upon unconsciousness is a death sentence for high level barbarians. I don't think that's a fair way to rule, but if you're the dm and you want to rule that, make sure your players know before they make their characters.