Insect damage, herbicides, high tomato yields or strong winds are the likely culprits of broken stems. Diseases don't cause broken stalks, although they may weaken the plant making it vulnerable to damage from other causes. Plant disease-resistant tomatoes in full sun and water them weekly to promote healthy, vigorous plants.
Stalk borers are creamy-white or purple larvae that bore into the stems. If the stem is withered or bending but not broken, look for an entrance hole and slit the stem directly above the hole. Remove the borer and destroy it. Bind the stem with electrical tape or soft fabric and keep the plant well watered. It may recover, depending on how much damage was inflicted.
Look for cutworms on the soil surface. They are brown, black or gray and may be 1-1/4 inches long. They bore into tomato stems at ground level causing the entire plant to topple. Tilling the soil several times in the spring destroys cutworms that are overwintering there. Wrapping a 3-inch, was paper collar around the base of newly-planted tomatoes, securing 2 inches of the collar beneath the soil's surface protects the plant from cutworms.
Exposure to 2,4-D and similar chemicals may be the problem. Herbicide damage causes distorted leaves, twisted stems and deformed fruit. A strong wind or storm might bend or break weakened stems. Herbicide damage may occur by using a sprayer previously used for applying herbicides for applying pesticides or fertilizer. Even if you avoid herbicides, drift from 1/2 mile away can reach and damage plants.
Tomatoes grown in grow boxes produce an abundance of fruit because of the rich soil and a constant supply of water and fertilizer. Tomato vines, especially small, determinate types, are not strong enough to support such heavy yields. Thin some of the tomatoes to lighten the load, or stake the tomato stalks. In a regular garden, yields are generally not heavy enough to break the branches. However, a large harvest of tomatoes combined with strong winds might cause damage. Stake or cage tomatoes if you live in an area with frequent high winds.