Damping off happens ... I have heard that weak cold chamomile tea helps stop this, but better still is using sterile seed starting mix for starting them. They like moisture ... but make sure they are not soggy.

Fireraven9
March in the garden - my hostess shows me brown sticks and speaks of flowers
- Sister Benedicta

Here is a link that might be useful: Growing Tomatoes

I agree that they might be too moist. Did you remove the cover once they emerged from the soil? If not, do so. They need the air. They need to dry out before watered again. Also, water from the bottom. Sunlight isn't going to be as strong as setting up some artificial lights and the lack of lights might be contributing to their problem.

I agree with the other comments. Let them dry, then water again from bottom with weak chamomile tea. I have had better luck with my plants started from seed since using the tea instead of plain water.

Read through the Growing Tomatoes forum for excellent info on this issue and lots of other tomato tips.

Hope they perk up!

Never had that problem, only the opposite. Are you sure they are getting enough light? Do try lighter, sterile mixes as those might also help.