Although we cannot know why no equivalent to the Meiji Restoration ever arose in China, there are some factors that we can say might have been responsible for this difference.
First, the Japanese were much more aware that they might need to change. China had always been the “Middle Kingdom” and had always felt that it was superior. Japan had a long history of changing in response to outside influences. This could have made Japan much more likely to embrace some sort of radical change.
Second, Japan is much smaller than China. What this meant is that essentially all Japanese could be aware of the seriousness of the Western threat. People in inland China could have easily discounted the idea that Westerners were a real threat to China. Japanese people essentially all lived near coasts and all knew that they were under threat.
Finally, there was serious tension in Japan between different ideas of how government should be conducted. There were those who wanted imperial government and those who wanted a shogunate. In China, there was only one way of governing. There had been many dynasties, of course, but there had only been one system of government. This meant that there were no Chinese who were hoping to change the system of government and there was no figure (like the Japanese emperor) who could give legitimacy to an entire new system of government.
For these reasons, a Meiji Restoration was less likely in China than in Japan.
The Qing government remained largely conservative and proved unwilling to adopt Western technologies and ideas, as rapidly as the Japanese state had done under the Meiji Restoration. In their eyes, the West were still viewed as barbarians - Chinese cultural pride was simply too deeply ingrained in Chinese society for them to stoop down to the level of the barbarians to learn from them. Such attitudes blinded many Chinese officials and prevented them from seeing the need for fundamental change in China. There was thus no significant industrialisation and little willingness from the Qing authorities to abandon their traditional imperial institutions, since that would only severely weaken their political power. The government in China at that time was simply too conservative and backward-looking in nature to have undertaken an effort as great as the Meiji Restoration, in China - they only sought to retain their power and to repel the West by isolating China from foreigners.