I get the sense that the show stayed away from illness for the same reason it stayed away from death (with a few notable exceptions) - because it wasn't really what the show was about. After all, its about older men (and later women) having fun in their "golden years," so stuff like death and illness doesn't really fit, though there are occasional episodes where somebody we never saw passes away. So nobody major gets sick and their deaths are mentioned later or not at all, except of course for Compo.