Even at S Skullduggery there's still a chance to fail if you don't waste an intersession to talk to the servants. It's only with DoL+ and getting past that where it pretty much becomes guaranteed (SSS).
If you hate the randomness of the event showing up and then the randomness of chance of failure, you can always savescum via the History Loading thing you can set in Options. Do Dances up until a point you're happy (whether the bare minimum to make them happy or just before you think the audience is going to jump you), then get off the Stage and Search the mansion. Event doesn't show up? Reverse to back on the Stage, do one more action and then repeat. Eventually you'll get the event and have it fire off properly; if not then you might need to wait for the next intersession if you still have more and you're at a point where the crowd is going to jump you either way, or as mentioned try another week. I mostly do the savescumming because being pulled to chop carrots in the Kitchen is a total waste of time and doesn't even give you Housekeeping; I'd rather steal from the two NPCs making out or from their vault room (especially if I haven't gotten the Artifact from there yet).
Note that saving the hostage causes the Dance job to end on the spot, which of course means you don't get the chance at beating (or taking on) the horse/centaur at the end for the extra money. So once you're done with the request for Jordan, while you can still go back and find another hostage (some other random NPC instead; I think it gets replaced by an Orphan instead of a Temple member?), it might be something you decide to savescum away instead if you're milking that Dance job for all the money you can.
