If your farmers got sick and there was nobody to heal them, it wouldn't take long before there was no food. In addition to having trained farmers, it's a good idea to have 2 trained healers (in case one gets sick) - especially on the hard setting.

It's too late now, but the game log would have told you what happened each time you lost villagers. The game log is in the Virtual Villagers folder and is called ldwLog.txt. You must check it immediately after exiting the game, however, since it is erased and rewritten each time the game is started.

The bad news is that Island Events don't occur in villages where there are only children (and the GC is a child).