From the perspective of livelihood capital, we take examples of poverty-stricken families who have already withdrawn from rural poverty in Aba, Ganzi and Liangshan of Sichuan Province as research objects, and identify the stable poverty alleviation of poor households in deep poverty areas through the analysis of natural capital, human capital, material capital and financial capital. On this basis, we take dynamic measurements for stable poverty alleviation with the introduction of the critical value of the duration of withdrawal from poverty and the critical value of multi-dimensional poverty alleviation. We find that the incidence rate of withdrawal from poverty, stable poverty alleviation breadth index and the dynamic index of stable poverty alleviation all decline with the extension of the duration of stable poverty alleviation. And there are regional differences in the extent of decline in these indices. From the decomposition of stable poverty alleviation index, the dimensions of financial capital and human capital contribute a lot to the stable poverty alleviation. Per capita net income, medical security and income structure are three main contributing factors for farmers to get rid of poverty stably. Therefore, the long-term stable poverty alleviation of peasant households is the result of multiple factors.