What kind of potting soil are you using?

I use an organic mix made out of Peat moss, perlite, some mushroom compost and a sprinkling of worm castings.

The funny thing is that I use the same mix for all my containers/beds and every small plant I purchased from Home Depot/Lowes is thriving.

Appears that your seedling are damping off, a disease caused by several soil-borne fungi (7-8 different types).
Warm soil and excess moisture are a prime breeding ground for these fungi, which are always present in garden soil.

Commercial growers often treat (coat) the seed with a fungicide and follow strict procedures to avoid this disease. As a result, their plants are resistant to fungal attacks.

Control measures begins before planting the seed, by Pasteurizing the seed starting mix (Heat the mix to 160°F for 30 minutes in a conventional oven or Microwave). Tests indicate that Sterilizing the soil at 180°F for 30 min. does not appear to offer the same benefit.
After planting the seed, keep the soil barely moist and provide good air circulation. The germination and growth rate will be somewhat slower, but the seedlings will be healthier.

After planting out in the garden, provide only enough moisture to keep the plant healthy and growing. Overwatering can cause the soil-borne fungi to attack healthy plants. It may not kill the plant, but growth will be retarded.

Hope this helps.
Good luck!

Thanks Lady Wind Surfer! This is super useful. It does appear that my seedlings were damping off because - (a) I may be overwatering them and (b) I reuse potting soil.

I'm going to try to fix this by sterlizing the soil.

That's why I asked about the brand of potting soils. Some just hold a LOT of water, especially certain organic ones such as Jungle Grow. Mixing a little pearlite in can help too, and you can spray the top of the soil with chamomile tea to prevent the damping off. I buy tea bags at the $1 store for this purpose.

Thanks ggg. Are "damped off" seedlings lost for good? I read somewhere that even if they survive they usually end up as weak, spindly plants. Thanks