While not the actual question OP intended to ask, I would argue that sAAver awards actually do still exist, they just can’t be booked for AA only itineraries. But T and U inventory is still required to book AA flights either as connections to partner flights booked through AA or to book AA flights through partners. So even though we can’t book them in isolation through AA, I would say that this T and U inventory is still sAAver awards. At the very least, unless and until the community comes up with a better term for it. FWIW I put a J award to Europe on hold recently (like, a week ago) that included a domestic AA flight (U inventory) connecting to BA to LHR, and the email from AA referred to it as a “Business/First MileSAAver Award”. So while it could just be old language that AA has forgotten to change, I would say it speaks to the intent that sAAver awards still, technically, exist.

Now, what OP clearly intended to ask is, when does AA release low mileage awards (or, perhaps, awards which are a good value). To that question, I don’t really have an answer, other than just check constantly and hope for the best.