I've never missed a gig because of illness in 34 years, knock wood.
I've missed for a few other reasons, though.
When my parents died; caught in a blizzard on the way to the gig; flights grounded because of weather. I managed to call the venue and let them know the situation each time.
Once, I was doing a "reunion" show in Connecticut with my former partner, when I became sick on stage. Not puking, but I could feel a flu coming on, with a raging fever followed by the chills, headaches, cramps and the Hershey Squirts. Sweating one minute, shivering the next. The audience didn't notice it, though, and I got through the night.
Thank God for my partner, Tom O'Carroll. When I had to leave the stage to go to the head, I'd announce that "Tom is gonna do the next one on his own," or," here's Tom with another fine banjo solo."
he saved my underwear that night.

Seamus