There are a couple a ways that may cause the destruction of a cultural movement.

One of those factors that can lead into the destruction of a cultural movement is the creation of an unfavorable public image about that cultural movement. In order to do this image-damaging information may be given to media like the press and this will influence how that social movement is portrayed by the media. If this does generate a bad image of that movement in the audience than the movement won´t get any support and might then come to an end.

Another circumstance which is damaging to a movement is the inhibition of the supply of resources and facilities. Money, spaces and supplies are obviously essential to the prosper of any cultural movement. If the government feels like the movement represents a threat to them they can cut their supplies and then probably cause the movement destruction.

Internal conflict is also a cause of destruction in cultural movements. In a big cultural movement is usual to see people that have different ideals than others within the same main ideal and that may cause conflict. For example in the atheist movement it´s possible that some people see the movement in a more extreme way than others and say that for being atheist you need to be anti-theist. Naturally this causes collision of ideas and may even cause the end of the movement.

The media has also a big influence in this and I´m going to use an example of it: The Facebook algorithm makes you see publications of viral things and in fact during the time when the ice bucket challenge was viral you would see nothing but it and that caused the destruction of a movement against gender inequality that was generated because of a black person who was shot by a policeman.