From the description, the problem is most likely fig whitefly. This sap feeding insect has been established in south Florida for a couple of years but was only detected in Pinellas County late this summer. It can cause heavy and rapid leaf drop on some species of Ficus, especially weeping fig, Ficus benjamina.
If the tree is small enough that you can spray it, you may want to consider using an insecticidal soap or horticultural oil. Thorough coverage is important and some repeat applications at 7 to 10 day intervals will likely be necessary.
If the tree cannot be sprayed, applications of products containing imidacloprid (such as Bayer Advanced Tree and Shrub Insect Control) or dinotefuran (such as Spectracide Tree and Shrub Insect Control) can be applied to the soil. These products help to control the whiteflies without killing the beneficial insects that help to control the whiteflies. Even if the soil or oil treatments are made it may be necessary to follow up with one of these products.
Additional information can be found here:
http://mrec.ifas.ufl.edu/lso/IAWG/FIG/The%20Fig%20Whitefly.htm
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