I have been watering it so the soil stays moist but not wet and giving it sun for a couple hours a day... What is going on?

My best guess - you are way over-watering it and it isn't getting near enough sun. 6 hours minimum is recommended and tomatoes don't need constantly moist soil. In fact they are quite tolerant of getting a bit droopy before needing watering. Constantly wet soil deprives the roots of oxygen which they need as much as water. No oxygen and the roots die leading to leaf death.

It's in a container right? So water it till the water comes out the bottom of the container and then don't water it again until the soil is dry down to the level of at least the length of your finger.

And arrange to get it much more sun if possible. See if it doesn't perk up. When it does a nice dose of 1/2 strength fertilizer will help. ;) Good luck.

Dave

How big of a container if it is in one? What soil did you use although I agree, oxygen starvation sounds right.