I ran across this article from a couple of years ago rather recently (someone linked to it during a discussion on another board).
It explained how and why Prohibition both happened when it did and why it was repealed when it was.
Basically, it came down to this:
1. Before 1913, about 1/3 of the Federal Government's revenue came from liquor taxes, so no matter how much the Temperance folks would yell, Congress turned a deaf ear to them.
2. In 1913, however, the US Government decided to try out something new for revenue: an income tax. This resulted in a lot more revenue than originally thought and it made liquor tax revenue irrelevant, so they were now willing to listen to the Temperance folks, and they banned alcohol.
3. Then in 1930, the Great Depression hit, and one area that it hit hard was income tax revenue. By 1933, the income tax revenue had fallen 60% and they didn't know when it would end, so they decided that the best way to increase revenue was to repeal Prohibition and tax liquor again.
Not that this should be surprising to any of us. As we all know, when it comes to government, it's all about the money.