Why did so much time elapse between the first and second waves of feminism?

It was because the first wave of feminism were mostly the rich and didn't want to protest or do any actions that lead the downfall of their reputations

Most of the women that were in the first wave of feminism were upper class women that discouraged and did not let lower class women join the movement. Because of this there wasn't as much women protesting leading to a downward directing protest. As the second wave came around there were much more problems brought to all women. this lead to a much more bigger and much more longer movement which in the end wound up extremely successful. so to answer your question the first wave did not last long due to discouragement and less support, less organization, and less people involved in the movement. Plus the opportunity was perfect for women in the second wave to show that they are not inferior beings and are very capable of the same job that a man can do.