I'll make this easy.
Last at-large bid by team and year:
Wichita State 2013
Southern Illinois 2007
Northern Iowa 2006
Bradley 2006
Creighton 2001
Indiana State 2000
Missouri State 1999
Evansville 1999
Illinois State 1985
Loyola 1968
Drake has never received an at-large.
I think this list is a little bit meaningless because of so many teams having years in which they would have received an at-large bid if they hadn't won Arch Madness. For example, Creighton the past two years, UNI in 2010, Drake in 2008, etc. There's no reason to punish a team for taking care of business in St. Louis.