I would suspect bacteria if its water based, They make ozone purifiers for your holding / cistern tanks if your concerned with your water quality for your personal health.
Im going with too dry or bad environmental conditions like too much light because they shouldnt dry out every other day other than the very top which should be stopped by say daily misting. I think moving up the light is your best bet.
Whats the high low temp of your room and the humidity?
High temp - about 78 under the lights.
Lows - around 60 but depends on outside temps.
Humidity usually under 30%.
I am not sure if it is any how related to your case, but I have two kind of plants - peppers and cabbages that catch fungus every year I plant them. I changed soil ingredients several times, sterilized the soil and equipment, even used ozone generator to sterilize grow room - no difference , every year it is the same outcome - peppers get powdery mildew at stage of 4 leaves, but so far I didnāt loose any. They recover when they get outside. Cabbage is a different story. It grows OK until it gets to 2 leaves stage. Than cotyledons start wilting from edges to middle, then leaves do the same and plant dies. I believe I have some kind of fungus in my growing environment that thrives without actual sun. So my solution is to start cabbages outside and plant peppers late enough to move them to greenhouse as early as possible. Also I spray them with Actinovate every week. But what people saying about moderation in watering is absolutely correct. I use syringe to water baby seedlings, it helps to keep it moderated, never, even just after watering, it should look like the water is standing, like on your picture, it should look dump, but not soaked. For the length of the root, do not worry. Most of the healthy seedlings develop central root in really no time, it is usually reaches the bottom of seedling cell by the time cotyledons are completely opened.
Do you know what the pH and hardness of your well water is? Is it possible that you have soft water? It could be softer this year after all the rain.
Just guessing, but in a peat based mix if you have soft water with little calcium to buffer it, the mix could be moving to a lower pH as the tannins are released from the peat. That would explain why it happens over time, not right away.
If you think that might be the case and the seedlings arenāt too far gone, you might try putting some fast acting lime in your watering can and mixing it around to raise the carbonate hardness of your water.
Galinas, that is EXACTLY what happens to my brassicas, but no other plants suffer from it. Like your case, it does not occur if i start them outside. So strange. Ive sterilized the area and all equipment with bleach but nothing seems to help. Frustrating. Let me know if you figure it out.
they will certainly find the water if it is there. i bottom water all of my potted plants and the top of the media is never wet.
Temperatures seem okay and i assume you are leaving the lights on 24/7. What kind of lights are you using and have they been successful growing other plants (mainly asking this if they are LEDs) and how far are they away from the seedlings, I leave mine pretty high for seedlings. I definitely think if that isnāt them yellowing from drying out you should try some sort of beneficial bacteria spray be it actinovate, double nickel, compost/casting or chamomile tea. If its yellowing from drying out i assume your light is too intense.
check the roots, they will tell you what you need to know.
I leave them on for 16 hours and off for eight.
I still start them every year just for curiosity, may be some day I will solve it 
.
I wonder if there is something in the environment of my basement thatās causing the problem.
Because last year, you may recall that even my tomatoes got these weird curled leaf issues, that nobody could really figure out. Yet, the moment they went outside, even as I was hardening them off, it went away.
They grew just fine after that once I planted them in the ground.
These issues seem to be mostly confined to plants Iām growing in my basement. When I started plants in another room of the house, I didnāt have this problem. However, that other room is both:
A. Too warm
B. Wife nixed it
So basement it is. 
I am also a basement grower and have the same problem in what should be an ideal environment: strong lights, lightly fertilized, watered adequately. I suspect that it might be cold air temperatures, lack of air flow and lack of some kind of beneficial soil biology.
You should try adding a tiny oscillating fan and worm castings next year and see if that helps.
Cucumber, melons and basil seem particularly sensitive to whatever is happening. Tomatoes, peppers and even flowers pull through pretty well. I also notice the problem usually happens right around the two leaf stage and then goes away whenever I up-pot (if the plants make it that far).
Definitely leave your lights on 24/7 for seedlings this reduces temperature fluctuations (unless you need them for things like hardy geraniums etc). I do understand the give and take our counterparts do for understanding yes im taking up this entire room with surprise plants we will get them planted when its done snowing and that we also need to be accommodating. Maybe more air movement would help in the basement and make sure there is no CO as thats bad for us and plants. Its obviously some sort of rot since you have checked most other issues and i would treat it or try reseeding them when you can outdoors.
I had no trouble with brassica seedlings until i moved the operation from the extra bedroom upstairs to the basement after baby was born. Same lights same mix same everything other than location and therefore different temp, sunlight and humidity, although the basement temps seem fine. Very strange. Could be the lack of sunligjt. I should move it back upstairs now that baby is older to see if the problem goes away
Could be the lack of air movement cause it too
I have whole house to my plants - sunny south-east windows, fans, lights, everything. Only thing I canāt do is to provide cool temperatures at night. But still same result.
i always have a oscilating fan on over my plants. even seeds need fresh air.
My concern about using a fan is that for the warm weather stuff like tomatoes, Iām actually relying on the heat from the light to make it warm enough for them, at least during the day. The ambient temperature of 60Ā° is too cold for tomatoes. They will grow slow as molasses at temperatures like that.
If I blow air through the room, itās going to make it too cold for the tomatoes, isnāt it?
Could it be excessive salts? I just remembered that the mix I use had Osmocote added to it. I added it because I was going to use it for my container trees. I separated it from the stuff I was starting seeds with, and I was down in the basement tonight and I think I actually mixed the two batches up.
I think I got it mixed up with the non-Osmocote stuff. Although conventional wisdom says that with CRF, itās almost impossible to āburnā a plant.
