Is this a plant that will only grow this year, or do you keep it year round? (I have friends in the Sonoran desert of Arizona who had a tomato that was a woody shrub because it never died off in winter!) I suspect the length of the plant's life might be important in this answer. A tender plant may be handled differently than a woody one.
Is this problem on all of your tomatoes, or just on one tomato plant? If the others are healthy I would be inclined to pull this one out and get it as far away from the healthy plants as possible. And take the leaf litter up so the problem doesn't travel around the garden.
There is a blight this year that is causing the fruit to rot, and it has been in the news a lot. I read on Martha Stewart's blog that her farm was hit by it. http://www.themarthablog.com/2009/08/the-tomato-blight-in-my-garden.html
She posted a lot of photos from this summer. Is this what your plant looks like?
The remedy for this is pretty ruthless, by taking out the entire sick plant, bagging it and sending it to the landfill, not putting it in the compost. I don't remember if Howard has said something similar.
Making sure the plant gets foliar feeding in the early morning and using a fish fertilizer is a good way to discourage red mites. A separate spray of orange oil will discourage a lot of other pests. Clean up the leaf litter under the plant and make sure it is well mulched. And don't over water it.
This is just a start, I'm sure there are others who can fine tune this advice. But please, tell us more about your garden and the nature of gardening in Costa Rica. And post a photo or two if possible.