When was the last time ut missed a bowl game?

That was the 1974 season. Michigan's record that season was 10-1 and they were co Big 10 champions. However, this was at a time when the Big 10 only allowed one conference team to go to a bowl game, that being the conference winner that would go to the Rose Bowl. That edict was discontinued in 1975 and Michigan wound up going to the Orange Bowl while Ohio State went to the Rose Bowl.