OK, how could Makhno's Anarchist movement have remained in power in the Ukraine after the Whites were defeated by the early 1920s ?
I've thought about this at length before, and I don't think there's any real way they can - at least, not under Makhno.
Makhno's "Free Territory" was a
temporary autonomous zone; it could only survive for as long as the two nearest forms of state authority were distracted ... fighting among themselves. Grassroots support for Makhno was born partially from war-weariness on the part of the Ukranian & Crimean peasantry, who took arms to defend their lands from the pillage and looting of various marauding armies.
A slightly weird & tangential way of achieving your stated outcome would be to have Makhno swallow his pride
much earlier, adopt a more conciliatory / pragmatic tone with Petrograd, and ally with the Bolsheviks against the Whites, in exchange for some level of regional autonomy - something like Xiaoping's
"one country, two systems" idea.
And then, if we can somehow manouvre a faction like
Group of Democratic Centralism or a "softer" version of Trotsky's
Left Opposition into a stronger position than OTL, slightly earlier than OTL, we might be able to circumvent Stalin, and find ourselves looking at a slightly more pluralist radical revolutionary alt-USSR, with Makhno and his ilk a tolerated (if not key) part of the political equation.