On reason we keep children home when they are sick is so they do not spread their illness to others. In a homeschool environment that is not a concern. A child with the sniffles can still do math and English since there is no worries of spreading germs. Often homeschooling moms will not provide time off unless the child is very sick. That is not cruel in the least. An illness where one can still function means they should still function even if you change your routine a bit.
In my home, unless a child is very sick or cannot function, we still have school. I allow the condition of my child to lead the day. If my child is fatigued then I allow for ample amount of rest. If my child has the flu then they can lay down on the couch all day watching mom approved movies and forgetting school exists for time being. I have never seen a reason to take a day off school for a cold. However, I am sneaky about it. When my child wakes up and I know the illness is mild, I just simply go on with the day as normal. If I hear a complaint about being tired or feeling bad then I address it. I find that my kids just assume they will work through a mild cold or a rare bout of pink eye. Once I sense fatigue then it is immediately time to rest on the couch watching a documentary. School is only called off completely during a flu. I am not being cruel. I am simply being realistic. I make no demands. I simply take their lead. I have noticed that my kids are more likely to maintain a steady stream of work ethic and not make how they feel an issue because we simply move along with our day. Again, I guide this and listen to their condition. Even in cases of a mild cold, if my child expresses feeling bad we take a break. My oldest rarely takes a break and will even read her school work when she has the flu all on her own. I think it is one more way to encourage a strong work ethic. Even if I feel weird about expressing it since it may come off as me being a mean mommy.
In my defense, unless I feel like I cannot move, I still work, teach, and do laundry.