@Onyxangel24 I know this post is 8 years old and the game in question is 12 years old but I still love this game and play it even today. I'm having the exact same issue with my Jacoban Priest. This responsibility never completes. I know it's the correct pirate because they have the orange map tag on them. I wear down their will to the yellow part of the bar, successfully interrogate them and... the responsibility doesn't complete.
A workaround I've found is to enable testingcheats (I have a tutorial on that on my blog which I'll link) and then whenever you get that responsibility in-game, CTRL+Click it. It will slam you with the shirked responsibility buff but you can then CTRL+Click away that buff to bring your focus back up.
It's not an ideal solution but it will at least let you bypass the bugged responsibility without sacrificing quest performance.
Here's the link on how to enable testingcheats in your game. If you don't want to mod the game, then just follow the second part of the tutorial to enable cheats:
https://snarkysims.wordpress.com/2020/09/23/how-to-mod-the-sims-medieval/#more-176 
