Prohibition did not succeed mainly because it was not supported by the majority of Americans. They simply did not see drinking alcohol as a "real" crime and so they had no moral qualms about doing it.
There are other factors that contributed to the lack of success. Prohibition did not actually criminalize the drinking of alcohol. Instead, it prohibited manufacture and transport and sale of alcohol. This meant that the average person who went into a speakeasy and got a drink was not actually breaking the law. Since drinkers were not really subject to punishment, they had no incentive to obey the law.
Those who did break the law had financial incentives to keep doing it. Bootlegging made huge amounts of money for organized crime. Therefore, the supply of alcohol was always going to be there.
Finally, there was not enough law enforcement manpower to effectively enforce the law. Agents were few and were not well paid. This led them to be easily bribed and/or evaded.
But the real basis behind the lack of success was the general idea that the law was a dumb one. Laws that do not have the respect of the people tend to be very hard to enforce.