AA 5564 then AA 6004 at Charlotte
Harrisburg → Charlotte → Gulfport
Timetable, Charlotte time
18:46AA 5564 from Harrisburg at the gate
15:58AA 6004 to Gulfport leaves the gate
21 h 12 apart on the timetable, overnight
AA 6004 leaves 21 h 12 after AA 5564 arrives on the timetable: more than half a day, so not a connection we count.