I see people say that he had it before fighting Fitzsimmons, but he beat the formidable Billy McCarthy just one year prior to fighting Fitz as well as beating the brakes off of George LaBlanche before the pivot blow. When did Nonpareil Dempsey get ill?
This article ( https://bklyn.newspapers.com/image/60729817/?terms=jack+dempsey+billy+mccarthy ) from prior to the McCarthy fight vaguely references "discouraging reports of Dempsey's health," which forced the fight to be postponed. I've read that Dempsey's health problems emerged following the Johnny Regan battle, which was fought outside in winter weather amidst rising tidewater.
Perhaps it was your typical injury? Hard to picture a man with tuberculosis going 28 rounds with a top middleweight, let alone winning.
Some time around 1891, I'd guess. https://chroniclingamerica.loc.gov/lccn/sn91070630/1891-12-02/ed-1/seq-3/
Seems like people were noticing it when he fought Fitzsimmons, either that or his showing was just that poor. That would mean that Nonpareil Dempsey drew (or maybe even beat by some reports) with a top middleweight in Billy McCarthy. Over 20 rounds, insane! Not sure how to rate Fitz's win over him now.
The postponement of his fight with Billy McCarthy in January 1890 was said to be because of flu but rumoured to be because of early symptoms of consumption. Of course, rumours aren't facts - people were terrified of consumption and quick to assume the worst. https://ibb.co/YpFbXC4