The advent of fuel cells has led to a series of studies on hydrogen production. As an excellent hydrogen carrier, methanol can be used for reforming to produce hydrogen. Copper-based catalysts have been widely used in methanol reforming due to their high catalytic activity and low-cost preparation. However, copper-based catalysts have been subjected to poor stability due to spontaneous combustion, sintering, and deactivation. Thus, the research on the optimization of copper-based catalysts is of great significance. This review analyzes several major factors that affect the stability of copper-based catalysts, and then comments on the progress made in recent years to improve the catalytic stability through various methods, such as developing preparation methods, adding promoters, and optimizing supports. A large number of studies have shown that sintering and carbon deposition are the main reasons for the deactivation of copper-based catalysts. It was found that the catalysts prepared by the modified impregnation method exhibit higher catalytic activity and stability. For the promoters and supports, it was also found that the doping of metal oxides such as MgO and bimetallic oxides such as CeO2-ZrO2 as the support could present better catalytic performance for the methanol reforming reaction. It is of great significance to discover some new materials, such as copper-based spinel oxide, with a sustained-release catalytic mechanism for enhancing the stability of Cu-based catalysts. However, the interaction mechanism between the metal and the support is not fully understood, and the research of some new material copper-based catalysts in methanol reforming has not been fully studied. These are the problems to be solved in the future.