Here are a few that give the Lady Vols a run for there money in longevity:
US 4x100 Olympic relay team--DQd in 1912, 1960, 1988, boycotted in 1980. Won the Gold Medal in every other year during that span.
UNC Women's Soccer--15 national championships between 1979 and 1999.
Iowa wrestling--15 NCAA team championships, 45 individual titles, from 1978-1997.