Why do stems on a tomato plants turn yellow, have brown spots, and then fall off?

Question

First the brown spots appear and then after a week or two, the stem turns yellow and then falls off. Does anyone have any ideas on what I should do?

The plants are producing fruit on the other stems, but my plants are starting to look bare, no longer full.

Answer 1

Tomatoes are so easy to grow, taste great but they also fall victim to so many diseases, most which are soil-related (too much water, too much shade etc)

Enclosed is a good summary of what could be ailing you.  Watch the growth habit of the spots and note how the plant is dying to elimate diseases that don't apply.  In the plant world, how a plant dies and the colors the leaves turn can be indicators of certain diseases.