My first couple of tribes died mysteriously so now I am very careful before I leave a game on overnight or longer, even on half speed. I have not had the problem since. What I do differently is that now I will only do it if I believe the island seems stable. If the island doesn't seem stable I will put it on PAUSE and come back to micromanage it at a later time. Or - at least - I will back up my files in case something goes wrong.

What I consider stable is:
* more than one doctor with "healing" checked so that they are free to heal. I am more comfortable with more than one because the doctors more than any other profession seem easily distracted and I don't trust just one to heal in case of an outbreak overnight.
* I watch the food levels for a few minutes before shutting off to make sure it looks like the levels that the villagers are collecting food outweigh the consumption. This is easier of course with higher food levels and one or both of the key food puzzles solved.

If I don't have a doctor or two with "healing" checked as their preferred skill, or if the food gathering-to-consumption ratio isn't right, I won't risk leaving it on.

This has worked 100% for me so far on this second tribe. I have a population of over 60 now and have solved most of the puzzles, after having a rough start with my first tribes. Good luck!

Oh, another thing you could consider, though I haven't tried it, is that if you do leave it running over night, check the "easy" button and then move it back to "normal" after you open it up the next day. I don't know, but it might help with less chance of sickness, etc.