I suppose I could give more details.

The leaves, starting at the lower ones, are turning brown and then dying, followed closely by the branch they are on. This is only happening to the Black Prince varieties at the moment. The tops of the plants are green, and healthy, blooming and fruiting, but the branches on the main stalks are all dying.

Amana oranges near by have yellowing lower leaves, I think due to fungus as well.

I am no good at diagnosing tomato diseases, hence my numerous posts here for help..:)

But one thing I can i.d. right away is spider mites. We have horrible spider mite probs every year here with tomatoes and I see the tell tale speckling on your green leaves and possible some webbing in your pic.
Spider mites can and will suck the life from your plant and I think some of the undiagnosed wilting that I get (which is very similar to your pic) is from the unrestrained/uncontrolled spider mite infestation.

here is a helpful link:

Here is a link that might be useful: spider mite websites