Kiev suffered in the 13th century economically since the trade with Byzantium was cut off until 1276.
1327, Constantinople fell after a long siege to the Rum-Seljuks, effectively defeated by the hunger. Many Byzantines fled, some even to Kiev. They arrived 1328 in Russia, settled mostly in Kiev. The city suffered under the loss of trade with Byzantium (it wasn't much left after the resurrection of the Byzantine Empire), but gained importance as a cultural center, thanks to the influx of Byzantine scholars. Later, when a Kievan prince married a Byzantine noblewoman, and founded schools and libraries to plead her, this would become even more apparent.
In an alliance with Hungary, the Teutonic Order conquered the princedom of Halicz-Volhyn in 1375, which was divided between them. The Teutonic part became object of German immigration and germanization too, and later formed the province of Wolhynien. Some Volhynians fled to Kiev, which gained in importance by their influx.
The Russian Schism
In 1381, the western and south-western states from Smolensk to Chernigov elected the most popular of them, prince Vladimir V Rostislavich of Kiev, their leader, seeking protection against the Teutonic Order, the Kumans and the Hungarians. 1383, the patriarch of Kiev crowned Vladimir V Czar of all Rus. The difference between the South / West and Vladimir-Suzdal that already was apparent became even more outspoken. Main reason: While the West had to deal mainly with the Teutonic Order (and Novgorod in addition with Sweden), and the South with the Kumans, who had to retreat from the arriving Kara-Kitai (who had fled again before Arik-Buqa, it's complicated...), Vladimir and its allies looked more to the East, where the Volga Bulgarians and Hungarians were.
Thus, 1388 the Russian schism began. The metropolitan of Vladimir and the patriarch of Kiev excommunicated each other, driven by the Czar / Grand Prince of Vladimir respectively.
During 1394-96, the Black Death swept through Southern Russian states, decimating Kiev's population too.
In 1409, the last Rostislavich ruler of Kiev died.
Vladimir-Suzdal wanted to solve the Russian schism by war 1413-22, but Kiev and Chernigov allied with Novgorod and Smolensk against it, and managed to win. Vladimir-Suzdal had to acknowledge the patriarch of Kiev as leader of the Orthodox church again. The schism was thus ended.
1431, Kiev managed to conquer back the areas Hungary took from Halich-Volhyn in 1375, since Hungary had trouble with the Bohemian theocracy, and the current king wasn't that competent.