Complex sentence: During its first three decades the show proved popular with members of the World War II generation, but by the late 1980s, thst generation had started to die off, as did the number of stations carrying a Big Band format.
Split into simpler sentences: During its first three decades the show proved popular with members of the World War II generation. But, by the late 1980s the show's core audience began to pass away, as did the number of stations carrying a Big Band format.