If you ask the few rational fans down here, they'll tell you that this started with the 2001 SEC Championship game meltdown ("Curse of the Georgia Dome"), but I don't think it really started until Fulmer's first losing season in 2005; that year, they were preseason ranked in the top 10, and finished 5-6. What stood out to me that year was watching Troy Smith lead the comeback in Ann Arbor at a Knoxville sports bar while at the same time, Jay Cutler came from behind to beat Tennessee and keep them out of a bowl game for the first time in about 20 years. That was also the first or second win for Vandy over Tennessee in my lifetime.
They just never evolved as the SEC got deeper in the early/mid-2000s. They were so used to ruling the league in the 90s when it was a two team league (along with Florida).