The city doesn't get sacked because... eee .... eeehm... well, you know... it so happened that... ughm
Hell, I quit...
Damn, I cannot imagine a situation, a PoD, or a shitload of PoDs, when a city so close to the Mongol steppe
doesn't get sacked.
Actually in OTL all this territory was devastated, razed to the ground, burned, depopulated, it was a hunting ground for the Mongols, till the Lithuanians somehow managed to form some kind of protection.
In this region it did not make any sense to sow - as nobody was sure to have a chance to reap, and the cultivated field will catch unwanted attention of the nomads. So the locals preferred alternative occupation like fishing or something.
So, if you want to give Kiev a chance - avoid the Mongol conquests: Chengiz Khan got killed by a stray arrow when young, this kind of POD.
Than Kiev has a
good chance to stay a cultural center of *Russia, it was a seat of all Russian metropolitan by the way.
I am not sure about being the political centre though...