In 1952, the members of the Small Brewers Association, the trade and lobbying group for the nation's smallest beermakers, decided that the word "small" did not accurately reflect the prestige of the association or its 150-odd members. (At the time, there were some 300 breweries in the U.S.)
Time for a new name. Henceforth, the SBA, which began life in 1942 as the Small Brewers Committee, would be known as the Brewers' Association of America. The BAA survived until 2005, when it merged with the Boulder-based Association of Brewers to become the Brewers Association.
Source: Modern Brewery Age 48 (September 1952): 79.