My daughter (with Canadian passport) stayed in China for a year. Usually what happens is that your kid can stay there for up to 180 days with his/her visitor’s Visa from Chinese Embassy. Before that Visa expires, you can ask your relatives in China to go to the local public security office to extend the visa (they call it Foreigner’s residential permit - Wai4Guo2Ren2Ju1Liu2Zheng4). It costs 200YMB and is vilid for about one year. You need yo apply for this, otherwise you have to pay for a big fine.