I will take a shot. I haven't had seedlings droop or flop unless something is wrong. The ones that I did have droop had been eaten by Fungus Gnat larve. They are tiny tiny white worms. They eat all the roots off the young plants and they will eat all the inside of the seed turning it into a dry shell. If you find this is your problem, let me know and I'll post a solution, or atleast something that really slows them down.
Oh yes, also, I had a few that were broken off by a silly frog that lived in my greenhouse. But these were broken off in the green leaf, not down in the crown or roots.
Do you have cats??? I've heard that they will sometimes try to eat the young green babies.
Ok, I know that there are more reason for leaf droop, so maybe someone else will help. I do agree that a picture will tell alot.
Hope this helps, Mona