• A Present from the Solitary Glim-sculptor, A Visit from a Cloaked Stranger - both of these cards seem to disappear once you accept their Fate-locked option. It is possible that I just coincidentally have not drawn them, however. Losing the Glim-Sculptor costs you gifts of inconsequential amounts of Glim and a free boost to SotC up to a certain point, and so I was not sad to see it go; losing the Visitor costs you a ready source of Laudanum and Tinctures. You can always buy them from the bazaar in a pinch.
• I am at level 9 on the Certain Plant story. I am given to understand that ripping the plant out will exchange four cards (noted orchid-grower consults, green lodger, green project, sprouting companion) for one (Where Did That Come From?, which restarts the sequence). This is at the cost of being able to participate in the Tournament of Lillies, a source of 10 beetles at a time, a source of 1CP MW, and a card that is pretty much totally useless. I should really just accept that I don't care about the Tournament and go ahead and do this.
• The Intimate of Devils cards all go away if you sell your soul. I assume the opening card will come back if I get my soul back- I don't know if there's a way to get rid of these cards permanently (does Abstration make them go away forever?).
• Nuking a Connection below 5 causes its Connection vs Connection cards to stop showing up. That said there's value to most of the connections at some point or another. So I haven't done this because I don't know which one I might not want sometime later. I guess Revolutionaries is one of the safer (and easier) ones to nuke? I use Docks and Widow for the Acacia; Urchins for this time of year and also as an easy thing to trade in for Docks and Widow; Society and Bohemians are important for the Salon; Criminals for Improbable Penance (though this is less important now that I am done needing Bejeweled Lenses for now); and I like having the occasional Menace reductions and Someone Is Coming gains.
  
• Remember the Honey-sipping Jewel Thief goes away if you kick him out of your life forever, which costs you the possibility of getting committed to him (I'm already married to my RL partner), and a source of ostentatious diamonds, which you can otherwise buy for 25 cryptic clues, so no big deal.
• Similarly, the Artists Model. This costs you a poor source of cryptic clues. My problem is I don't like being unnecessarily mean to people. It'd be nice if you could tell them to go away without having to insult them. :P
• Various purchased pets have related cards. It is up to you whether you think they are worthwhile or not. I always hesitate to get rid of them in case there's a card down the road that wants one to unlock an option.
  
• I assume A Letter From your Aunt goes away too if you do the Fate-locked option. I haven't done this one.
• Cards for specific Visitors stop showing up if you no longer have their acquaintance. Given some of their specific storylets and options I am loathe to tell them to bugger off.
• I suppose NOT buying every damn lodging in the game would keep the deck lean and mean, but it's too late for that, and hey, scraps are good.
• Getting a Remote Lodging gets rid of the City Vices cards. I'm not sure if any of those are worth keeping. I do the Decadent Evening one if I'm actually making a push for Notability but I wouldn't cry to stop getting it; I'm not sure I ever do any of the others.
  

Yeah, I've heard one of them has a chance of refreshing your actions. Not sure if it's all or just 10 of them, though, and while I have heard that it's better now than it was before I've never done it so I can't speak from experience.