I hate making those calls!!
I have had some really great families in that regard, though. I think all in all, I have not had to close that often, but when I did they were great about it. I also tell them in the beginning (interview) to ensure that they have backup care should anything happen. The reality is; I have 4 young kids, we are going to get sick sometimes!
I for sure push through it more than I would at a "job", I think. One time, last year; I was up ALL night with my oldest at the children's hospital (literally not a wink of sleep). I got home in time to shower and grab a coffee, then open up my doors. When the daycare parents learned about it they all said "Are you crazy? Why didn't you just call, we would have worked it out!!"
I thought about it from the parents perspective and realized that I would NOT have wanted someone to care for my kid in that condition!! So that made me feel a little better about when I do need to close.