I developed an overactive thyroid several years ago, but had it treated with radio-iodine. Now it's underactive and I have to take medication daily, but I only have to take one pill on an empty stomach. I usually wait until right at sunset at take it, then pray Maghrib and then break my fast. I do feel a bit woozy and slightly lightheaded by that point, but I know I'm going to have something to eat soon. Now, if it were a case where I had to take medicine twice daily at let's say 12 hour intervals, I think there's no way that you could avoid having to miss fasting.