I have had the same problem of seedling leaves turning yellow and dropping off. I have a few seedlings which are just stems but some also have new growth sprouting all up the stems. The slightly older seedlings with bigger leaves have less of a problem with this but some do have nute burn around the leaves. So after reading this post it's hit me that the problem is obviously too many nutes, either from the soil or from what I've been watering into them.
I originally potted them with a bag of the cheapest potting mix the hardware store had (yes I know.. big no no) and have been watering in different nutes to try and correct a deficiency they had from variagated yellow and green leaves. I tried lots of things like using tap water left out instead of filtered water. I also used an aquarium bubble stone to aerate the water. I saw positive results from magnesium sulphate and using the bubble stone, but then they got the all over yellowing leaves and leaf drop. I think the bubble stone made all of the nutrients available to the plant (or something like that), which corrected the deficiency but there was too much and it created an excess.
The advice I have seen on this site seems to be overwhelming that seedlings need little to none nutrients. I am prone to overfertilizing so it makes sense that too many nutes are causing this leaf yellow-drop problem. I'll pot up the ones that survive into a neutral mix after rinsing the roots, then feed them a very restricted diet. I'll save the overfertilizing for my basil plants, they take everything they can get and more.
Yeah, I don't know...
The thing is, I've started adding some fert to some of the plants (about 1/4 strength) and they seem to be doing a bit better than their brothers and sisters on a water diet. But I can't say anything conclusive since I only have a small sample (right now 5 babies + 1 stem). But what I can say with some confidence is that it doesn't seem to be hurting them - and I'm definitely not seeing any fert burn. So...although overfertilizing/overwatering seem to be the most talked about villains, I don't think they're my villains. Really the only thing I've yet to test is the ph of the soil (because I'm to lazy to get a kit). That's what could be making the babies suffer from nutrient deficiency despite the soil being (too) rich in plant food.
And you know, so far I've been only able to grow the Red Savinas, which were from the same source and the same bag. So...I can't really rule out that the seeds might not have been in the best shape. Especially since all the Bhuts and all but 1 of my yellow burkina habaneros (which were the other two types of seeds I ordered) failed to germinate and some developed nasty looking black stuff. I'm currently in the process of germinating about 40 seeds from a different supplier so I'll be able to say more when they pop up.