The powers countered by Outwit would still be countered until the beginning of the next turn of the player that activated the outwit power, so there wouldn't be much of a use there.

Under Indy rules check that the Outwitted power returns only if Outwit is lost (not appearing in the dial anymore) or the figure is KOed, it doesn't talk about the power being canceled.

QUESTION:

If E Batman outwits someone when in it's first outwit clicks, and gets smacked enough in one hit to pass to his latter outwit clicks (losing it mid-way the damage clicking), is it considered to not having lost the power thus the power would be still countered?

You can turn off team abilities when MCing but they can be turned right back on at the next action. So If you MC Batman and shut off his stealth, then after the MC try to attack him w/ range, he can turn on his stealth again as it is a new action.

Taking into account that:

Then, Team Ability cancellation works just like Power cancellation, thus staying canceled until the end of that turn. There's no reference in the rulebook for the "turn back on" option to any player after the Power and / or TA has been canceled.