Social stratification is a means of organizing (and limiting) access to power, prestige, and privilege in society by assigning an arbitrary value to certain attributes. Some forms of social stratification, like India's traditional caste system, are closed in that they have rigid rules which limit mobility. In the United States, socioeconomic class is a little more mobile and changes in a person's wealth or social power can affect their SES status. That being said, seemingly mobile, open, or fluid class status often comes with some hang-ups based on the present structure of stratification.
One of the features of human culture is that it is constantly undergoing transformation while retaining an element of continuity. The best way to understand this is through language. If you have grown up speaking the same language as your grandparents, consider some of the ways in which your particularities of speech differ. Do you always use the same terms and phrases? Do you know slang words that they don't? Probably! However, the general rules of your spoken language have most likely remained the same.
Social stratification persists because of the "general rules" of society that we have learned to function in, under, and through. Change in social stratification and the justification thereof does happen, but it can take a lot longer than just one or two generations to really be visible. Below I have attached a diagram which lists some of the ways social stratification and injustice may be perpetuated in society. Remember those "arbitrary values" I mentioned before? In most stratified societies, it has been determined that certain genders, biological sexes, races, ethnic identities, languages, religions, health status, and ancestries are preferable to others. The devaluation of certain identities is performed and experienced through the acts listed in the diagram below, and cyclically justified based upon those arbitrary values.
In order for social stratification to persist, these arbitrary values have to be taught and believed by the uppermost portions of a stratified society. It takes active un-learning of these arbitrary values for a society to really take action to remedy stratification. Without devaluation of one or more identities, social stratification cannot be justified.