Ser Cortnay Penrose reads "During power challenges, Ser Cortnay Penrose gets +2 STR and gains vigilant." Vigilant says that after you win a challenge, you can stand all vigilant cards. Here's the situation: Ser Cortnayu Penrose is knelt. I make a power challenge with a different character. If I win, would Ser Cortnay stand? During a power challenge, he has vigilance, but when the challenge is over he is no longer vigilant. Would the vigilant response go off before he loses his vigilance?

Yes he would still stand. He doesn't have to be in the actual challenge for him to stand. Just anytime there is a power challenge he has vigilant. Vigilant would go off before the challenge ends, so he would stand.

Note that Vigilant is a passive keyword effect, not a Response.

However, all passives and Responses related to "winning/losing a challenge" are considered to take place as part of (or, more to the point, within the duration of) that challenge.

Think of all the "after you win a challenge, choose a participating character..." Responses. If the Response didn't take place within the duration of the challenge, there would never be a participating character to choose.