Young plants come up but grow long, thin spaghetti-like droopy stalks, then inevitably die. Here you can see I've tried propping some up, to encourage them to stand up. Why is this happening? I'm using a commercial Burpee seed sprouting kit with expandable peat pellets. I guess they're peat. They're getting plenty of sun and some are getting lots of water, some little, but it doesn't seem to make much difference. Same result always.
If you really wanted to try to save those get a pot and burry them deep in the pot and cover the stem with dirt up to the leaves. Straighten the stem first though
Bringing them in at night may be your problem. Do you always get them back outside at the same time the next day? Are there lights on inside of your house at night that may mess with these seedlings? Growing them under CFLs until they develop a few leaves may be a good idea. Put them into bigger pots and put those spiral light bulbs close to the seedlings and they will get stronger and grow some before you put them outside.