I know that for most international fares there is a provision for illness, but I don't know much about domestic fares.
I've had rotten luck a few times of getting really sick before or during travel (probably because of my constant exposure to kid germs - I'm a 5th grade teacher) and the only time I've ever been penalized was by BA.
However, having flown FRA-LHR-JFK once while sick with a serious upper respiratory and ear infection, I would much rather pay a penalty or fare difference or whatever than repeat that misery.