How would a character lose Flurry before making a second attack? Similarly, how would a character lose HSS before it finishes moving?

principally Mistycs damage and critical miss but also are some special powers if i'm not wrong

Mystics, Crit Miss, Steal Energy, special powers.

Ah ha. That makes sense. Thanks for the clarification.

A point that is often overlooked: losing and then regaining HsS (or Flurry) will still end the effect of the power.

Ultraman has HsS and Steal Energy on click 1, but does not have HsS on click 2.
Ultraman hits Mysteriogirl, who has the Mystic TA.
Mystics and Steal Energy have the same timing, so the active player (Ultraman's controller) chooses the order.
He chooses to take the Mystics first, going to click 2, and then the Steal Energy to bring him back to click 1. But since he went to click 2 as a distinct event, he lost HsS and cannot continue moving.