AA 5967 then AA 5335 at Charlotte
Baton Rouge → Charlotte → South Bend
Timetable, Charlotte time
16:23AA 5967 from Baton Rouge at the gate
15:48AA 5335 to South Bend leaves the gate
23 h 25 apart on the timetable, overnight
AA 5335 leaves 23 h 25 after AA 5967 arrives on the timetable: more than half a day, so not a connection we count.