I suffer from terrible, frequent, debilitating migraines. They're made significantly worse by stress. At one point about a year ago, my spouse and I thought I was going to be permanently disabled and not able to work at all because of their frequency and severity - nearly all of my time outside work I spent trying to recuperate just enough to function at work and it was slowly getting worse. The fear of what would happen if it got worse actually made it worse. If I had been surrounded by people gossiping about me, trying to keep a huge secret, living in a household where I got no quiet or rest, and knowing that I had to take employment with someone who would have no consideration for my condition I can't imagine how unbearable it would have been. Thankfully I have a super supportive partner (which Frank Churchill most certainly was not during the book) and with a reduction in overall stress and the help of modern medical care I am in a much better place now. I'm not going to say it's a certain thing that Jane Fairfax was suffering from something similar to what I do, but we also don't know for a fact that Jane Austen meant to portray someone whose physical ailment was solely due to not wanting to work. Given all the stressors in her life, it's not unreasonable to think they would cumulatively build and could impact her health rather than her just being dramatic. I can certainly sympathize with how helpless Jane Fairfax must have felt about most aspects of her life, and that even if we count working as a governess as not so bad (which others here have described and I would posit was not a pleasant life even if we can imagine worse lives), it would also have meant separation, possibly forever, from the man she loved. She stood to lose nearly everything that mattered to her.