Found this under Florida law on rabies
(2) A dog or cat shall not be required to be vaccinated against rabies if a licensed veterinarian has examined the animal and has certified in writing that at such time vaccination would endanger the animal's health because of its age, infirmity, disability, illness, or other medical considerations. Such exempt animal shall be vaccinated against rabies as soon as its health permits.
And it also seems in Florida, it can change from county to county on if required yearly or 3 yrs..
Good to know that about an animal with health issues - and yes, it does vary county to county. Hillsborough, where I live, requires it yearly.