Essentially two things happened which greatly reduced the importance of cities like Samarkand, Bukhara, Merv, Balkh etc, both of which took centuries to really fully develop. The first was the reduction of the importance of the Silk Road trade, which was mainly a result of the increasing importance of maritime sea routes for trade during the 1500s-1700s. The second was the growth of the Russian and Qing Chinese empires in the 1600s forward(and to a lesser degree a more powerful Persia in the 1500s and 1600s), each of which both opened new trade routes through their territory, and politically, militarily, and technologically began to dominate the region of Central Asia and the Steppes, ultimately culminating in most of Central Asia being incorporated into the Russian Empire. That said, this was a slow process, and the cities of Central Asia remained important and wealthy long after the end of the Mongol empire, and even generated further empires themselves-the Timurid Empire for example had its capital in Samarkand in the late 1300s-1400s. Ultimately however, the wealth of these cities depended on their central strategic locations in the silk road trade, and, much like other cities like Kaffa, Venice, Alexandria, Genoa, Jaffa, etc in the Eastern Mediterranean area who also depended on that trade, once its importance was reduced because of maritime sea routes, so was the importance and wealth of the cities on those trade routes. Without the silk road trade, the main basis for the wealth of Central Asia's cities disappeared.

Peter Golden, Central Asia in World History, Oxford UP 2011 is my main source here, I have a couple more but I don't have access to them right this second.