Even if the divisions of OTL are avoided, they need a genuine gunpowder army and probably enough of a settled peasant base to provide an infantry component by the mid-1600s at the latest. Not only were the bordering states getting better at using their own techniques against them (see Manchu banner armies, Cossacks), but vs gunpowder empires a high-mobility horseman-with-a-composite-bow based army was by early modern times becoming obsolete, only still really effective in steppe areas where enemy forces could not easily be resupplied by water or live off the land, and then more in a defensive than an agressive role. (Moscow being made out of wood was always a big help when sacking the city.

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The last successful Tatar raid on Moscow was in 1571: Russian forts ran all along the Kazakh border by the 1700s. Only its relative remoteness preserved Central Asia from Chinese or Russian conquest into the 1800s. And of course there is the problem of European states undergoing a demographic takeoff from the early 1700s on: if the Golden Horde's system continues to keep peasants off fertile land to favor horses, the manpower differential will get worse and worse. If they can keep Russia fragmented, it will be a big advantage: perhaps a long-term Horde-Polish-Swedish alliance to keep the Russian man down?
Bruce