Yea, keep an eye on it. Twice now I've had similar circumstances (although both were before I installed version .05)where my peeps kept getting sick. I kept buying the medicine that would cure what they had, but every time I went back into that household, one or more of them was sick again. I consulted a doctor finally and one of them was "gravely" ill. That's when I finally noticed that his health bar was almost at the very bottom!

Course, this actually happened back when I only have version .01 and was really new to playing but even so, it's best to make sure you do keep a close eye on it cause even if the doctor doesn't say it's serious now, it could become that way. Good luck!