What Makes My Tomato Flowers Fall Off the Vine
Stem directly behind the flower becomes dry and flowers easily fall from plant.
Certified GKH Gardening Expert
For both the tomatoes and peppers, if the buds fall off without fruiting, this is a sign of a pollination problem. These articles will help:
One of the things that make tomatoes drop fruit is periods of intense high temperatures. Something we seem to have a lot of lately. Keep them well watered. I use a epsom salt and water spray to help mine set fruit. (1 teaspoon of epsom to one quart of warm water, mix throughly and spray the plants) I have clay soil, so the extra boost from the magnesium in the epsom salts help my tomato plants set fruit more quickly.
Hope that helps.