Relevant rules:
2-7-1 A down is a unit of the game that starts after the ball is ready for play with a legal snap (scrimmage down) or legal free kick (free kick down) and ends when the ball becomes dead.
3-3-6-a-1 An official will declare a timeout and the player(s) must leave the game. That player must remain out of the game for at least one down, even if that team is granted a team timeout.
Scenario:
A34's helmet comes off through play (no foul, and he is tackled at the A-40 for a first down. A34 must leave the game for one down (2-7-1). During the following play, A64 holds B53 at the LOS, so it is A 1/20 from the A-30.
Since we are repeating the down, does A34 still have to sit out the down?
AR 3-3-6-II: II. After being treated for a bleeding or oozing wound, A22 (A.R. 3-3-5-I) attempts to enter the game before the next snap. RULING: A22 must remain out of the game for at least one play. In any event, he may return only on the approval of his team professional medical personnel.
According to the logic of the AR, no, he does not. I'm just wondering why the rule says he must sit out a down, not a play. And if (being extremely pedantic here) if that means he does in fact have to sit out more than one, if there is an accepted penalty involved where the down would be repeated. I know Elvis has given explanations on the difference between a down and play here before but I can't find it.
Probably just a dumb derp moment on my part as to why I'm eve asking this, but I did find it a smidge confusing, although I'm likely overthinking this.