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Originally I thought that the fact it said "one or the other Houses of Congress" might have something to do with this, since the House tends to be less able to keep up traditions due to the turnover in Representatives every few years. And I was almost right. Although the date looks to be slightly off, it turns out that:
February 19, 1979
On this date, William Hill Boner of Tennessee read George Washington’s Farewell Address on the House Floor—an annual tradition for nearly 50 years—for the last time.
Although it looks like this had been problematic for a long time, since apparently participation in this was falling off over the previous few decades.
Some Members questioned the annual ceremony, especially when participation began to fall off. In 1972, Teno Roncalio of Wyoming criticized fellow Members for their lack of participation, bemoaning the low attendance at that year’s ceremony: “Indeed, there were not more than 10 of us here at the beginning of the speech, a few less at its conclusion.” After the House discontinued the practice in 1979, Members observed a wreath-laying ceremony, held on the grounds of the Washington Monument until 2003.
I got this from the House of Representatives site noted below, and they give a little more on the tradition and how this was originally done by Junior Members, some who were the first's such as the first female Representatives from a state, first Asian-American woman who was the Representative from Hawaii.