From the info provided so far and assuming the seeds weren't infected the only thing I can think of is fungus gnats. Any sign of those? Check for aphids too.

Otherwise I would try transplanting them DEEP. Find a really deep container like a liter pop bottle with the top cut off and bury as much of that bare stem as possible into somewhat larger containers with fresh mix and then feed them a diluted dose of fertilizer. You can't count on the small amount of fertilizer added to the mix to feed them.

Dave

No aphids. I haven't seen any gnats flying around, but what other signs should I look for? Is it possible that I am letting the plants dry out too much, then when I water them, the branches swell up and break off? When I bottom water, I leave them in the tray of water until the top of the soil is moist again, then take them out and let them drain. Previous attempts I did leave the seedlings a bit too long and they wilted before watering, but these two seedlings haven't wilted. Thanks for your help!

Did lower branches wilt an fall off ? In that case the soil was to dry.

I would fertilize them with liquid fertilizer at 1/3 to 1/2 normal recommended strength.

Sey

No they didn't wilt prior to falling off - they looked normal, then the next morning were on the ground. I just repotted them, buried the stems, and watered them with 1/2 strength fertilizer. We shall see what happens :)

I used to develop gardening products for Scott's, who acquired Miracle Grow a few years ago. Miracle Grow was a fabulous product before Scott's - with a great fertilizer balance. But not now.

Scott's official policy is to require ALL their products to have far too much nitrogen because they tested consumer response to fertilizers years ago, and they decided:

1-The consumer is stupid.

2-If there is too much nitrogen in the formula, it is cheaper to produce, and the "stupid" consumer will be happy with the fast green-up from too much nitrogen.

Your tomato soil has too much nitrogen and the plants have too little water, and maybe too little light. They are struggling to GROW, GROW, GROW with the excessive nitrogen, but they do not have enough water to do it. Tomatoes are grown best hydroponically-in pure water. You are not watering enought.

Repotting deeper is important, but not in more nitrogen-loaded soil.

Get as much as possible of that excessive-nitrogen soil away from them without disturbing roots too much. Put them in good quality non-branded unfertilized potting soil. Fertllize with only low nitrogen fertilizer (5-10-5 is ideal.) Water enough that they do not drop leaves. And put in sun outside as much as possible to harden off for planting. They should have been in the ground before this if growing for outside.

If you are trying to grow permanently inside, try Tiny Tim, who requires less light.