Got this info today from the Master Gardeners and I thought I would pass it along.
Q. - I have a recurring problem with my tomato plants. They do really well until they start fruiting and then they start dying. THe oldest parts begin to turn brown and gradually the whole plant turns brown with just the fruit remaining on the branches. Any advice?
A. - The damage you describe is typically due to the tomato russet mite, Aculops lycopersici, and is a common problem in our warm climate. The damage starts at the ground level and moves up on the stems and leaves. The mites suck cell contents, first from the stems and leaves and later from the fruit. The stems and lower leaves dry out and turn brownish or bronze in color, then die. The mites are too small to be visible to the unaided eye.
Recommended controls, acceptable for organically certified crops, are sulfur dust and sprays. Apply sulfur dust when the winds are calm and wear protective goggles and a mask. Wettable powders are easy to apply with a hose end sprayer. Do not apply in hot weather, i.e., > 90Deg F.
A web search will bring up a lot photos showing the problem and suggested controls.
Hope it helps you! Doreen