Not really sure what you're doing, but you've got to train your villagers. Villagers die from old age or starvation. I suppose they can die from illness, too, but I haven't seen that.

You've got to keep them fed. In order to do that, you need to train at least one villager to farm. Start by picking one to be a farmer. Get his/her details and check farming to give him/her a preference for activity. Whatever activity you check will be the one they go back to again and again. You still have to train the farmer, though. At first, the only farming on the island to be done is foraging for berries. Place your farmer by the berry bush. He'll try to forage. He may be unsuccessful at first. You have to keep placing him there until he carries a basket of berries to the food bin. At the bottom of the screen, you'll see a few details about the selected villager. Note that he is "untrained". After he takes his first basket of berries to the bin, move him back up to the berry bush and keep repeating until he's no longer "untrained" but an "trainee farmer". From my experience, at this point, he'll forage on his own and move up the ranks to "adept farmer" and eventually "master farmer".

The berry bush, however, isn't enough to keep your villagers from starving. The only way to learn how to do more advanced farming is to do research and spend research points on farming. For this, you'll need to pick another villager to be a scientist and train him at the research table in the same way you trained the farmer at the berry bush.

The same goes with builders, healers, and breeders. Figuring out how many of each you want/need is part of the game. There's not a single combination that works, but different emphasis will make the game unfold in different ways, although always to and through the same accomplishment thresholds.

By the way, I like to train some of my villagers in different skills. You can change an adept farmer, for example, into a scientist by changing which skill is checked in that villager's details page. You'll have to train him or her anew in the new skill. I have found that once a villager has lots of training in more than one skill, he'll move back and forth on his own among the activities associated with those skills. Generally, he'll prefer the skill that's checked, but there's also a strong preference for the one where he has the highest degree of skill.

Hope this helps.