What you're describing was not actually originally a Chines hairstyle but rather one that was imposed on China during the Qing dynasty, the period in which those movies are set. The hairstyle, known in English as a queue, was originally a Manchu hairstyle and was something mandated by law shortly after the Manchus took control and began the Qing in the 17th century.

Initially it was primarily soldiers and officials who were ordered to shave, but later it was extended to the population at large. There were a number of reasons for why this was enacted, but put simply it can be seen as cultural imperialism and has often been argued as a way of determining obedience.

It was also not just limited to hairstyle. That was just one part of a larger dress code to get the Han Chinese more in line with Manchu practices. Later on, with the fall of the Qing, the cutting of the queue was thus equally symbolic to a population now free of Manchu rule. Thus what caused it to disappear was the fall of the Qing, that it was no longer mandatory, and that it came to be seen as a symbol or an old China that the new China was trying to move away from.

Also, since we're on the topic: the Chinese dress called qipao/cheongsam was originally Manchu fashion as well, despite now being seen as a distinctly Chinese fashion.

Is there any subreddit for qipao/cheongsam?