Damping off usually hits very small soft seedlings and kills them quickly. Southern blight will rot stems at the soil line once they get planted outside, but you can see little pink or white fungal blobs on the stem.
Dig down and uncover the stem and see if it is brown, shrunken and dead. If so, the plant will stagnate but not die for a long time because it still gets water from the roots. I have had seedlings of both peppers and tomatoes get broken by wind at that part of the stem during hardening off, and I planted them deeper with success. Roots grow out above the dead zone. I don't know if that would work if it is disease. Cutting them off above the infection and replanting in fresh mix might work. but I would be certain that the stem section is dead first