The steppe nomads may have been poor and primitive, with one-twentieth the population of China, but they had the advantage of mobility:
When we moderns think of the advantages mobile horse archers have over infantry armies our minds jump to the tactical — Parthian archers wheeling about at Carrhae, Mongol faux-retreats, and their like. However, for most of Inner Asian history nomadic mobility had its greatest impact at the strategic level of warfare. The nomads had no population centers to defend. They had no walls to guard and did not have to worry about holding key strategic points. When an enemy force threatened their homes they could simply pack these homes up and move them somewhere else until the danger was over. If an enemy army could not be beat in a pitched battle then the nomads would not fight a pitched battle. They would retreat, disappearing into the desert or grasslands until the enemy was forced to return home. These retreats and migrations took a toll on the nomads’ herds, but it did not bring them to economic ruin.
The same was never true for the Chinese. The economic costs of any expedition against a nomadic foe were enormous. To call a soldier on a campaign was to take him away from a farm; the state not only had to pay him for his service but had to do so with a smaller tax base. The state also had to feed him while on the campaign. The bigger the force the more supplies needed to feed it. The steppe is hostile to invading armies; there are few farms to plunder or cities to loot. Everything the army will eat on the campaign must be brought with it. This means long supply trains. The further the Chinese chased the nomads into the steppe the longer and less protected these supply trains would become. Eventually the invading force would reach a point where their supply lines could be stretched no farther. If at this point they decide to turn around and return home then they have wasted their entire treasury and gained nothing from it. On the other hand, if they try to hold their position the nomads will circle round, cut the supply lines, and leave the invading force to starve in the desert. The Chinese are offered a grim choice between retreat and death.
Worst of all, once the invaders have returned home and disbanded (or if they chose death and were all slaughtered in the desert) there is nothing to stop the nomads from returning to the border and continuing on with the standard raids, surprise attacks, and pillaging nomadic warriors are famous for.