Rule 11D (as modified) does not indicate how long a period of time may elapse, after his opponent completes an illegal move, during which a player is still entitled to receive the 2-minute penalty. However, 11D1a seems to say that, in sudden death time pressure, it is only until the player has completed two more moves.
This apparently means that a player can complete a response to his opponent's illegal move, wait for his opponent to reply yet again, and then decide whether or not to claim a time penalty. Even though the penalties have been standardized for non-sudden-death, it is not clear if there is still a separate distinction for "sudden death time pressure" for going back two or ten moves for illegal moves, and if the window to claim them and receive a time penalty is the same for plain sudden death, as opposed to "sudden death time pressure."