If my character outwits my opponent's power (example probability control) and the opponent's character moves to a position where there is no longer line of site from mine to his, does his character gain back that ability for that turn?

Thank you

No. Line of fire is only needed to activate Outwit, but once countered the power is gone until the beginning of the Outwitter's next turn.

Or until the outwiting charachter loses outwit either through taking damage, or having his outwit countered. When this happens, the countered power returns immediately.