I talked to my brother about this a few weeks ago. He went to Georgetown for law school and lived/worked in downtown DC for 9 years.
His response was basically that people there don't actually care about the college team. Undergrads at Georgetown come from all over the country and leave after graduation. He was friends with very few people who cared at all about Georgetown sports. They have tons of history and none of it matters. He compared it to the university of Miami and football: lots of history, lots of success, 5-10k people show up to their home football games