Confucianism

I think there are three reasons why Confucianism has an enduring influence in China.
First of all, Chinese rulers had adopted his philosophy in ancient times not just in politics, but also in education and social. Second, it was a compulsory subject to be studied in school in ancient times. In fact, the Chinese started learning the Confucian classics since young and imperial examination is largely focus on the subject of the Confucian classics. Third, Confucianism proved to be effective in making a dynasty longer-lasting, instead of say legalism. For this reason, many dynasties follow what previous dynasties had done, and continue to adopt it as a philosophy.
It's why Confucianism has an enduring influence in China.