You might check on the Tomato Growing forum. I suspect that it's either the heat and humidity causing flowers to abort, or else the plant is still young and not ready to set fruit.

George
Tahlequah, OK

I am having the same problem. The plant is really healthy and I am getting nice strong bright yellow flowers and then suddenly the stem breaks off a 1/4 inch in from the flower head and it falls off. Yet the stem is healthy, its not thin or browning or weak, it just breaks off. And when it breaks off the inside of the stem is still white and sappy. I phoned around different garden specialists and they say it must be the temperature, either its too high or its too low. I don't know if I agree with that.

I'm probably late with this response but I have the answer, I think, to the brandywine tomato problem. I asked the question on another forum and I received the response from another member that I should use an electric toothbrush at the base of the flower where it joins the stem, just behind the flower. I have just been trying it for the last 4/5 days and so far no blossoms have fallen off. I have my fingers crossed that it will work.

I was wrong. The electric toothbrush didn't work. The heads are still falling off. Unless I wasn't doing it the right way.