That untrue, Leader keeps their effect for the whole battle.
I've seen it happen every time Ashigaru was used in battle. Once hes played, I get to act first the next hand. Since I have no leaders of my own, thats what I base it on.
I think Ashigaru's ability is opp plays first on the first card -- not on every card.
Ashigaru's ability is that you go second on the first fight. In other words, you'll play first in the second & fourth rounds when Ashi's one of your 4.
Leaders work through all the fight even if attacked/blocked by stop.op.ab. cards. Ashigaru is different , his skill makes you play second in the opening round. That doesn't sound that impressive but you still get a 8/6 card , best leader's stats and one of the nicest cards around (esp the looks)