Flopped Anagallis (Pimpernel)

I'm having so much trouble with Anagallis Monelli. I sowed the seed and have about 50% germination. The seedlings shoot up pretty quickly in a tall, thin stick with 2 tiny leaves on top. But they get to a certain height and just stop growing, and after several days of looking the same, they will suddenly flop over and shrink until dead.

I started in a sealed container in a dark, warm place. Then I tried a cooler place in different soil that I let get SUPER dry after germination. The stem grew in thicker this time. But the others hadn't germinated, so I put just a bit of water over the others, away from the good one to keep the soil dry. At the same time, the temperature outside (a bit of it blowing in through the window) got cooler but still above freezing, down to maybe 55*F inside.

Over 24 hours later the weather is warmer, and the tall stem is horizontal.

Is there somethign I'm doing terribly wrong, or was it the day of cooler temps or the slight moistening of the soil around it?

I have 2 seedlings in another container that seem to be doing well, but am worried it'll happen to them too.

Once they germinate they need light--without adequate light they will tend to be very floppy and leggy. The shrinking until dead part could be damping off, it's a fungal infection that is a very common problem with seedlings. If that's what is going on, then you are probably watering too much. But letting the soil dry out all the way could also kill the seedlings. (I wasn't entirely certain from your message exactly what treatment the seedlings that died got vs the ones that are still alive)

The first set were kept very moist and low light
The second set had more light and were dried after they germinated, and kept that way. I watered the soil somewhat near to them and the temp dropped a little and 1 day later they flopped and died.

The third set is still alive. The soil was moist to start but gradually got drier and is getting a little more sun than the second set.

In 1 and 3 I put a little peroxide in the initial watering to sterilize it a little more.

I haven't had a problem with damping off with the rest of my seedlings, just this anagallis. I hope I don't have to start a 4th set.

I had to start a 4th set, and they did absolutely nothing.

So I started a 5th set and so far they aren't germinating either.

This flower is the hardest thing I've ever tried to grow and I don't know why. I started them Feb 25, and It's now May 10, and I'm back to square one. WHYYY?

Maybe try directly planting them in the garden--mine reseed themselves nicely without me having to do anything. They don't reseed to the point of being a pest (like their cousin Anagallis arvensis) but I get some new babies every year.