Thank you kindly.

But, Outwit itself was never lost. The source may have changed from one click to the next, but the character's ability to use Outwit was never countered or lost, so I would assume that the effect continues.

If a character has a power that grants you use of Outwit, like the one the Leader has with I CAN'T STOP YOUR BRUTE STRENGTH, BUT MY MIND IS FAR SUPERIOR (ICSYBS,BMMIFS), and he loses that power, then all the effects from that power end. If he is turned to a click that has the Power Outwit, then that is a separate and different power from ICSYBS,BMMIFS.
Don't look at it as the effects a Power gives you, look at the Power on the dial.
I CAN'T STOP YOUR BRUTE STRENGTH, BUT MY MIND IS FAR SUPERIOR is lost: Outwit is gained.

I agree that ICSYBS,BMMIFS was lost, but The Leader had the use of the Power Outwit both before and after the damage was taken. I don't understand how that constitutes losing and gaining Outwit.

Assume a figure had outwit on clicks one and three, and not on click two; they outwitted something, if they take two damage (from outwit past the click of no outwit to outwit again) the effects of their use of outwit would not go away - both before and after taking the damage they could use outwit, despite the click in between where they couldn't. That transition didn't matter to the fact that they never actually lost the use of Outwit.

This is a different matter entirely. If they start on Click 1 and are damaged to Click 3, the character is not considered to have been on Click 2.

If a character has a Special Power that grants the use of a Power in it, then the granted power is an effect of the Special Power. If that Special Power is lost, so are all the effects that it grants.
If an effect of a Special Power is granted by another Power, it is still a different Power.

And I really want to use a different example, because the Leader's Special is really, really long.

But, what Power is showing on the Leader's dial on Click 1?
ICSYBS,BMMIFS
If the Leader is damaged onto Click 4, does he lose that Power?
Yes.
If he loses that Power, he loses all the effects of that Power, including the use of Outwit.
Leader gains the Power Outwit on Click 4.
Is Outwit the same Power as ICSYBS,BMMIFS?
No.
The Power he Possesses changes from Click 1 to Click 4. He loses one Power and gains another. When he loses the first power, he loses the effects it grants. The use of Outwit is lost, then gained back, but the Special Power was still lost. Any Countering he did with it would be gone.

I was going to criticize you for picking a character with an acronym long enough to be a sentence.

Do you also support the HELPING CHILDREN THROUGH RESEARCH AND DEVELOPMENT charity?

Fair enough I suppose.

It still looks to me like the figure can use Outwit and never loses the ability to use Outwit, thus the countered power should remain countered. That isn't to say it hasn't been explained clearly, you've covered why it goes away quite well, I just don't agree with that interpretation of "losing" the power when it never goes away.

We could always switch over to AvX Emma Frost and "It's Her Decision" (IHD) if we wanted to shorten the acronym.

You seem willing to switch to that other power, but you should check with Dairoka. It's His Decision.