In all likelyhood, what is required is a weaker Kievian Rus, or one that for some reason feels the need to focus elsewhere; problem is that "elsewhere" means in general less valuable preys, except Byzantium, and the Khazars would need Byzantium anyway.
However, in the eyes of the Russians controlling the steppe to their southeast to some degree is going to be a priority for understandable reasons. This does not mean they'd be succesful just beacause they've been OTL. The key was the Byzantine shift of alliances, when Rus appeared to them more reliable, (and the Khazars less hostile to the Caliphate than before).
So, IMHO, surviving strong Khazaria means weaker, or differently oriented (Baltic?), Russia.