I just turned 34 and I cannot remember an undefeated home season. Last year it was Syracuse. In 2010-11 they went unbeaten at home in conference but lost to UK and Drexel. In 2009 it was UNLV and UConn. 2008, a bad Cinci team. 2005 UK and Memphis. And before that the teams just really weren't that good. In 93-94 they managed to lose to Kendrick Warren and VCU. Throughout the 80's they lost at least one home game. After a little research, it turns out that 79-80 was the last (and possibly only - I didn't check) time Louisville went undefeated at home.
Several prestigious schools routinely go undefeated at home. It's disappointing the Cards haven't pulled this off in going on 35 years.