I've worked out that, regardless of your BEST efforts, villagers will die anyway. I've also found that it isn't such a bad thing.
I spend sooooo much time searching for mushrooms to appease the hungry tribe. When your tribe members die down to smaller populations, you don't have this issue.
I've found that a tribe of 8 or less means that my villagers are more productive, tasks are completed more efficiently (you can argue whether it is faster but I think so as the larger the tribe, it seems the larger the mass about the food storage and the minority staying on task), AND most importantly - they are much less likely to run so short on food that they die of starvation.
Allowing your population to decrease also helps you to increase your villagers in their parenting skills. I found my tribe members were constantly procreating and making my population unsustainable.