The Question for you is what does the board think is more plausible and has the greatest potential, between the varied Central Asian Empires which had at least a settled movement among itself.
First allow me to clarify terms. By survival, we refer to the particular empire surviving its initial threat in the POD given. Continuation, refers to lasting a fair period of time afterwards, this however must be achieved with continuity in administration, thus a new dynasty is allowed, but the empire's perception must remain the same (such as China or Rome or the Caliphates of the Arabs).
Thus without further adieu, the empires that we will be choosing from,
The Kushan empire POD 200 CE. The stipulations is to make the Kushan survive the period coming and also maintain its grip upon Central Asia. Bonus points if the Kushan can capture Tocharia and reinvigorate the Silk Road on the decline from this period on, or remedy its troubles in India.
The Hepthalite Empire and its vassals, POD 500 CE. The stipulations if for through some method, that the Hepthalites survive the Sassanid-Turkic alliance and either maintains its borders and powerbase where it exists or reforms itself as a principle power/empire within India (in effect as the Mughal Empire or the Ghurids/Delhi Sultanate).
The Qara Qhitan/Liao empire in Balasgan, 1150 CE. The survival rules are that the empire must resist the Mongol hordes and subdue the Kwarzemshahs through some method and form an empire claiming the Chinese empire but with borders similar to the Kushan Empire. Though if the poster feels more plausible the Mahakhitan cocnept more plausible, then this also is accepted method of survival.
The Kwarezmshah Empire, POD 1219 CE. Survival stipulates defeating the Mongol hordes and remaining the dominant power in its domains. Continuation refers to the Kwarezmshah creating a continuity in the region as opposed to what it was, a sort of haphazard collection of appendages.