You are one demanding client
.
1982 - #1 Old Dominion lost to #4 Kansas State in the third round(Kansas State would then lose to Cheyney State 93-71).
#1 Long Beach State lost to #4 Drake
1986 - #1 Virginia(the year after they lost their dynamic assistant coach) lost to #8 James Madison in the second round
#1 Georgia lost to #4 Tennessee in the third round
1992 - #1 Tennessee lost to #4 Western Kentucky in the third round
#1 Iowa lost to #8 Southwest Missouri State in the second round
1998 - #1 Old Dominion lost to #4 North Carolina State in the third round
#1 Texas Tech lost to #9 Notre Dame in the second round
#1 Stanford lost to #16 Harvard in the first round
2001 - #1 Tennessee lost to #4 Xavier in the third round
#1 Duke lost to #5Southwest Missouri State(Jackie Stiles) in the third round
2010 - #1 Tennessee lost to #4 Baylor in the third round
#1 Nebraska lost to #4 Kentucky in the third round
2013 - #1 Baylor lost to #5 Louisville in the third round
#1 Stanford lost to #4 Georgia in the third round
2014 - #1 South Carolina lost to #4 North Carolina in the third round
#1 Tennessee lost to #4 Maryland in the third round
(you asked of the previous 27, but this year is thrown in for good measure)