TL;DNR: Look at your HOA's governing documents, not Florida law.
Under Florida law, "The officers and directors of the association have a fiduciary relationship to the unit owners." As fiduciaries, they are legally required to act in the best interests of the owners. Florida law adds many specific requirements to this general duty. These include carrying enough insurance, maintaining an adequate reserve, and handling money and records. However, the law is silent about the HOA's duty to maintain or repair the property. These duties are covered in the HOA's governing documents.
The HOA's governing documents such as the Declaration and Bylaws, are not easy to read. They are likely filled with boilerplate, standard provisions written in the worst legalese. But somewhere in these documents are maintenance provisions. These will tell you exactly what the HOA must do when property is damaged. They certainly require the HOA to repair damage, and say exactly who must pay for which repairs. They may even set out damage levels that trigger different actions by the HOA, and set time limits on when the HOA must act.
The Board is legally required to follow the rules laid out in the governing documents. If it does not, you can take it to court to force it to do its job.
Before you dive into the Declaration and Bylaws, you may want to read this lawyer's answer to the question of what owners can do to force HOAs to maintain property.
(If you have termites, you probably also need to look at the HOA and owner's insurance policies, and any pest-control contracts.)
Big Caveat: It likely won't be enough to simply read the Declaration and Bylaws and insurance policies. What exactly they mean depends on how Florida courts have interpreted Florida law, and similar condo documents. Court decisions will be especially important in complex cases such as this, where the damage is confined to one unit, but the fix involves everyone. In this situation, you may find it useful to do more focused searches on line, or talk to a Florida attorney. (A quick search for termite + Florida + Condo + HOA gives a lot of reading options.)