Are there people who cannot handle living in hot humid tropical climates? People who will get constantly sick?

6 months? Really it depends entirely on the symptoms, but if it's bad enough where the person would easily classify themselves as "sick", and it is negatively affecting their quality of life, I would say that's too long to simply be the "tropics" - it sounds like some form of immunodeficiency issue. I would see a doctor.

Yes.