It sounds incredulous that Liao even survived,considering it’s surrounded by much more powerful states and that it’s power structure was quite fragile as well.Hmm that's hard to say. The first novel did have a somewhat huánghàn tone. In the second one though I didn't feel much of that.
One factor I can think of is, the founding emperor of Xia warned the Liao chancellor Han Derang 韩德让, that the Liao empress dowager (who was close to Han Derang and depicted as a former lover of his) may try to harm his wife and son out of jealousy and political calculations.
Han Derang was somewhat persuaded and sent his wife and only son (Han Chang 韩昌, who didn't exist IOTL) to take refuge in Xia. The empress dowager demanded them to return, Han's wife committed suicide in order to not implicate her husband, and the boy returned to Liao out of his own ambition and grudge against both his father and the Liao state.
Han Chang then refused to inherit his father's position, powerbase and Khitan-Xi subordinates, and led his loyal Han and other minority subordinates to the further northeast. He waged war against the local tribes there (who were constant troubles for Liao even IOTL), earned a repuatation and steadily rose to the highest commander in Liao's 东京道 (Eastern Capital Circuit, approximately in today's northern Jilin and Heilongjiang). Then he revolted when the tide turned after his father's death (the Khitan aristocrats were long unhappy about the power Han Derang as an ethnic Han had). He dealt heavy casualties and losses to Liao but ultimately failed. This led to further discrimination and oppression against Han and other minorities that followed Han Chang, and Yelu Dashi as a proud Khitan was probably not the same guy he was IOTL as a result.