I think it's worth pointing out that under the command of Ögedei, the Mongols did conquer the Korean peninsula, and the Mongols are a recognised Chinese dynasty (the Yuan dynasty), so you could almost make the case that the Chinese did conquer Korea. Unless you mean specifically the Han Chinese dynasties, but in that case I'd like to remind you that many Chinese dynasties weren't Han Chinese, the most prevalent being the Manchu.

The Han Chinese tried to subdue Korea during the Sui and early Tang period. Sui's military campaign was disastrous. Tang first allied with Silla and defeated the other two Korean kingdoms Baekje and Goguryeo. The alliance soon broke down and the two former allies fought for control of Korean Peninsula. Silla ended up taking over the Southern half of the peninsula, while Tang had control over Manchuria and Northern part.

There were many reasons why Tang could not take over the entire Korean Peninsula. But the most prominent one was simply that Korea was a very remote location to the Chinese. The earlier Tang-Silla alliance made provisions easier, but when war started between Tang and Silla, Tang had no ally close by to supply their forces. The harsh winter also made it difficult to sustain long military campaigns.

These difficulties made wars against Korea prohibitively costly. Tang also faced greater threats from Turks in the North-West frontier. Allocating resources to support conquest of Korean Peninsula became impossible. The subsequent Chinese dynasties faced similar challenges in the North.

After the Tang-Silla wars, Korean kingdoms generally maintained a peaceful relationship with the dynasty in China. The Chinese had greater threats like Turks, Mongols, and Manchus to deal with. So there was no incentive to conquer Korea thereafter.