Here, I'll try to give you more of a hand then other ppl. This is coming from memory, I haven't played this game in a few years.
There are many reasons as to why this might happen. From the sounds of it, I'd be looking into possible health care, fun, or ppl moving to the other colony for whatever reason. Make sure that when you click on your next turn that your food supplies are increasing and that you have enough air for people. If your skipping a lot of years, make sure that you have open your colony statistics window. Also, if the age group of your people is extremely high, i.e. 60 years old, then you'd have a problem. Also, usually it tells you how many people are dying in a window.
Whenever you make drastic construction make sure your colony statistics are open, especially during population booms.
As far as the manual is concerned, I haven't read anything that has to do with plagues and cures and I'm pretty sure that the computer says something when your colony has one. I remember when I first started playing this game, I didn't know there was sub-levels; that you could build under the ground, lol.
Anyway, good luck. If you need any more help, let me know.