A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Veiled Menace Political Open: Target your unbowed Courtier: A target dishonorable Personality's controller loses 2 Honor. After each time the Personality's unit is assigned, his controller loses 1 Honor.
My question is this: does the effect last past the end of the current turn? I do not believe that it does but the "each time" wording opens the door for the effect to extend past the current turn.
does the effect last past the end of the current turn?
No, "each time" does not override the default "end of turn" duration.
Effects, Duration of effects, Ongoing effects: Ongoing effects last until the end of the turn in which they occur unless otherwise indicated. For instance, “permanent” or “until” a certain game time are phrases that override the default "end of turn" duration.