From what I can tell, Qing faced heavy humiliation, and lost numerous wars to western powers. But despite this, western powers took very little. Things like Hong-kong, maccau, Port Arthur, etc. Why didnt western powers take bigger chunks out of China like they did with Indochina?
Stephen Platt touches on this in Autumn in the Heavenly Kingdom, but at least in the case of the British, there was great fear that China would become the next India; ruling a completely foreign land with millions of subjects would be incredibly difficult. The sheer distance meant that it took two months just to get a message to China, and the military force necessary to keep China in subjugation would maul a budget already stretched by imperial expansion.
What the British were after was a stable market for manufactured goods (cotton cloth, primarily); to that end, it was much more beneficial to have a local state bearing the cost of actually ruling the country, while being afraid enough of Europeans to keep its markets open to British traders. It's a good way of maximizing profits and minimizing costs.
To add to /u/dandan_noodles, don't forget the massive land acquisitions the Russian Empire made in the Convention of Peking in 1860. The cession of Outer Manchuria was a huge deal for Russia ─ it allowed Russia to replace the rough port of Okhotsk with a viable port at Vladivostok, and construction of that port provided the impetus for construction of the trans-Siberian Railway, which extended de facto Russian influence over inner Manchuria as well until 1905.
You have to consider not only other countries relation to china but also the different countries towards each other. This is the best way to look at it.
/u/dandan_noodles has explained about Britain is correct. At the same time Britain wanted to make sure that Russia would not take more of china. Both because they wanted to keep the market open and because they wanted to limit the power of the Russian Empire (and later by expansion the Russo-French Alliance).
The growing power of the US also enforced china independence. The US did not want to outright conquer china but they did not want others to do so either.
Essentially everybody was afraid that if they tried to take to big a piece for them-self. So China slipped by without the faith of Africa or India.