You've just described my weather and tomato plants. The best I can figure, all the rain and humidity has provided the perfect conditions for fungus to thrive. I'm thinking Septoria lycopersici.
From: http://pubs.ext.vt.edu/450/450-711/450-711.html
Septoria leaf spot of tomato, caused by the fungus Septoria lycopersici, is one of the most common and destructive diseases of tomato in Virginia. The fungus can cause severe leaf spotting and defoliation is common following severe infection. Heavy leaf loss during wet seasons leads to sun scalding of fruit and failure of fruit to mature properly.
Symptoms
Numerous, small, water-soaked spots, which are the first noticeable characteristic of Septoria leaf spot, appear on the lower leaves after fruit set. Spots enlarge to a uniform size of approximately 1/16 to 1/4 inch in diameter. They have dark brown borders and tan or light colored centers. Yellow halos often surround the spots. Severely infected leaves die and drop off. Septoria leaf spot is easily distinguished from early blight, another foliar disease of tomato, by the uniform, small size of the spots and the lack of concentric rings in the spots; however, Septoria leaf spot is sometimes confused with bacterial spot of tomato. The presence of fruiting bodies of the fungus, visible as tiny black specks in the centers of the spots, confirms Septoria leaf spot.
Favorable weather permits infection to move up the stem, causing a progressive loss of foliage from the bottom of the plant upward. Plants appear to wither from the bottom up. Loss of foliage causes a decrease in the size of the fruits and exposes fruit to sunscald. Spotting of the stem and blossoms may also occur.
Chemical Control
Apply fungicides on a preventative schedule before the disease first appears on the lower leaves. Begin sprays when the first fruits of the first cluster are visible after blossom drop. Apply fungicides every 7 to 10 days or more often when the weather is warm and wet. In home gardens the fungicides, chlorothalonil (e.g. Daconil 2787) or maneb (e.g. Maneb), can be used.
After weighing my options of copper sulfate mix, ferrous sulfate, or a chemical fungicide, I quickly ruled out copper because I don't want to cause a copper imbalance in my soil... that and copper is toxic to everything (plants, fungi, bacteria). I didn't want to be burdened by wondering if I'm applying too much.
I went to lowes and reviewed the selection of fungicides. Many were neem oil based and seem to treat more trivial infections, which excludes septoria. Only one treated seemingly everything fungal, Daconil. So I bought it.
After reading the label and considering the degree to which I had to protect myself from the chemical, and after using it once and feeling a little trepidatious to work around the tomato plants, I decided to shelve the Daconil pending further research into its safety.
I settled on ferrous sulfate (Its called Copperas, its about $5 for 5lbs). Its safe for me and the plants, yet it makes things uncomfortable for fungi. Additionally, the iron and sulfate will help green the leaves. Due to heavy rain, sulfate will be one of the first nutrients depleted in soil because of its negative charge.
To enhance fungicidal activity and correct possible iron chlorosis of the grass, Cutting recommends adding ferrous sulfate to the tank mixture at a rate of 1/2 oz./1,000 square feet of turf area. Ferrous sulfate is an inorganic chemical of iron and sulfate, and iron is an important component of photosynthesis. "We've been using ferrous sulfate with our fungicides since the early 1950s to increase the green of grass and improve the finish of turf," he explains. Data show that when turf is under stress, particularly during hot summer months, the grass plants have difficulty absorbing iron from the soil. When applied as a spray, iron can be foliarly absorbed through the leaf tissue.
Ref: http://archive.lib.msu.edu/tic/holen/article/1982may4.pdf
Here is a study comparing 16 mixtures of fungicides for the control of early blight in celery: http://fshs.org/proceedings-o/1957-vol-70/134-136%20(DARBY).pdf
The result was Ferbam (sodium dimethyl dithiocarbamate + ferrous sulfate) is an excellent fungicide.
I'm not going to claim the ferrous sulfate by itself is an excellent fungicide, but it does have some fungicidal properties. I mix about a teaspoon in a squirt bottle with water. While out pruning off branches having yellow stems or clusters of yellow leaves, I keep the bottle with me and give the plant a good squirting.
Its important to remove the dead and dying branches, thereby eliminating some of the innoculum, and increasing airflow around the plant. I've even considered setting up a box fan in my garden.
I also prune branches growing in the middle of the plant or those which never receive sunlight. The idea is to open up the interior to airflow.
Is important to keep the plant healthy. This includes fertilizer with plenty of potassium and calcium. Lack of calcium causes blossom end rot. Lack of potassium generally produces brown spots (necrosis) and necrosis at leaf margins in a wide array of plant species. A good fertilizer blend for tomatoes would be 30% N, 5% P, 40% K, 20% Ca, 5% Mg. I'll leave you to decide how to mix your favorite water soluble fertilizer with potassium sulfate, calcium nitrate, and epsom salts to arrive at those percentages :)
The distinction between overwatering and too much rain is that overwatering is drowning the roots producing a condition of suffocation to oxygen and starvation of nutrients a plant needs, while too much rain washes soil nutrients out of the root zone, starting with the anions (NO3, SO4) and then affecting the cations (Ca, K, Mg, etc). If you have well-draining soil, you can water a lot and not produce root-suffocation, yet you'll wash away nutrients. If you have heavy clay soil, you can water a little and still manage to suffocate the roots. Root suffocation would be similar to yanking the plant out and tossing it on the ground... the whole plant will suffer. Rather, in this case we have healthy plants with the exception of yellow leaves on the bottom. This wouldn't be root-suffocation or overwatering, though, it could be that the rain leached away enough nutrients to leave the plant in a malnourished state, weak enough to succumb to a fungal infection.
Update
The more I contend with these sickly tomato plants, the more I think the cause is nutritional.
Consider this:
1) Why doesn't it affect the upper limbs until the plant has been severely weakened by the loss of lower limbs?
2) Why doesn't it affect fruiting limbs?
3) Why do symptoms only show after fruit-set?
4) Why does a fungus, which is naturally present in the air all the time, only attack sometimes and only some plants? Can a fungus be specific to only the tomato plant?
5) Septoria strikes after a wet season, which is conducive to fungal growth, but leached soil is also associated with increased rainfall.
My Theory
Heavy rains leach soil of calcium, sulfur, magnesium, and potassium (in that order - per The Nature and Properties of Soils – Harry Oliver Buckman, Nyle C. Brady). The leached soil leaves the plant vulnerable to disease while, at the same time, the increased humidity favors fungal infestation. This explains why lower limbs, the limbs less defended by the plant, are attacked first. It also explains why limbs not containing fruit are attacked first, the plant defends the fruit, not the leaves. And it also explains why the disease strikes most often after fruit-set, since the plant is having to divide its nutrition with the fruit.
Therefore the cause would be nutritional. The mechanism (fungus or bacteria) for decay isn't important.
My Treatment
I applied lime everywhere. I dusted the plants as well as covered the ground in liberal amounts. I want to accomplish 2 things with this. 1) To add calcium to the soil and plant (if possible). 2) Rain can have quite a low ph, therefore I want to neutralize that acid before it hits the soil. The acid rain will also break the calcium loose in the lime. A possible third effect may be to raise the ph on the leaves, making it uncomfortable for the fungus (if so, I would consider this more of a side-effect than the main idea).
I started fertilizing with calcium nitrate, potassium sulfate, and magnesium sulfate (epsom salts).
I also found this page to be interesting: http://www.aglabs.com/newletters/tomatoes.html
The bottom line is that if you are having disease and insects in your tomatoes, something is out of balance. The first things to check are your calcium and phosphate levels. For quick fixes, liquid calcium nitrate and liquid phosphoric acid can prove to be valuable aids.
I will update this answer as I discover more.