There are a few problems that might lead to the death of the citizens. The first and most important one is the temperature. If you don't mine enough carbon, the reactor will stop working. This will cause a drop of temperature in the city. This will cause its inhabitants, especially the homeless ones, to die due to frostbite.
Another reason why people are dying is sicknesses. They are directly related to temperature. Even if an inhabitant survives a cold night, he might become ill. If you don't provide proper healthcare, he will die. Because of that, you must have working medical posts that are able to heal your citizens.
The final aspect that might cause your people to die is the lack of food. You should focus on gathering food as fast as on mining carbon. Otherwise your men will die - the time of gathering unprocessed food and the efficiency of hunters' huts will be too low to produce enough meals.