Odds are they never did.

The earliest evidence of a stirrup-like device is in a few isolated images in Indian tombs of the 2nd century BCE, though they seem to be little more than modified saddle straps. The first "true" stirrup known was depicted in an early 4th century CE Eastern Jin tomb near Nanjing, China. The oldest physical evidence we have are in the tombs of the Xianbei, a people from the steppes of modern Mongolia. And, as you assumed, this made them quite the military power. After the fall of the great Han dynasty, China dissolved into a number of shifting political and cultural regions. The Tuoba tribe of the Xianbei was able to temporarily unify much of northern China under military rule, utilizing both light and heavy cavalry against the light horsemen and footmen to their south. The stirrup then spread through Asia, reaching Europe centuries later. So while the stirrup was extant in the world during the Roman empire, its armies would not have encountered any opposing heavy cavalries.

If you're interested in further reading, look at Lynn White's work on how the introduction of the stirrup lead to European feudalism- interesting theory.

Source: The Sitrrup and It's Effect on Chinese Military History by Albert Dein in Chinese Warfare to 1600