So you got Affection but aren't qualified for Love yet? If not qualified for Love you cannot rescue Saki.
1) Meet the Love requirements (Affection, Favor 5k, Obedience 5, Love 100, Hate Mark 0, Event: Tell Teru the truth - not 100% sure about the hidden requirements but they will turn white once fulfilled).
2) A [152] "Protect the bond" command will appear in the menu when you are ready.
This will disappear if you forget to do it and lock the love route.
3) Type 152, confirm and execute the Sumire-Teru Great Lovey-Dovey Operation.
If you fail to rescue Teru's sister (Saki) within 10 days, she will be sold as a slave offscreen and you'll be stuck in this state (you'll get a bad end on the 11th day that plays as a cutscene). This will also be reflected in the conditions by the event being dark crimson and clearly showing "impossible to obtain".
As stated in the wiki, you cannot unlock other hidden abilities or stores after this so if you somehow wanted Forbidden Knowledge (as a completionist considering what it does) do that before hearing the news from Awai Oohoshi. You can still develop lewdness and even slavery, though.
One bad end that isn't mentioned is if you develop Teru too fast, as she procs her lewdness events *before* she can proc the affection one and then cannot proc affection anymore if she climaxed like a beast (the game will get confused about her discovering masturbation). This is a bug and isn't reflected ingame, so you're just stuck with no further explanation if this happens and can't unlock anything except lewdness.
Edit to not bump the thread: Slavery while lewd and in love (all 4 traits) will also lead to the most twisted happy ending. You first need to confirm that you want to enslave Teru then you can either stop or dig deeper into the insanity.