I have a policy that they are picked right away if they throw up once, have a fever, are too miserable (because of being sick) to participate in daily activities, and any contagious illness...such as pinkeye.
For things like pinkeye, which is very contagious and very uncomfortable for anyone who gets it, they are not allowed to return unless they have had treatment for it for at least 24 hours.
I wouldn't want my family or other dck's getting it, or any of the dcp's to find out that I have allowed an infected child stay at daycare.