I had the same issue. Once your coconuts get down to miniscule levels, they'll stop climbing the trees and harvest the crops.
I was down to only 6 coconuts on the trees and they still wanted to pick them, instead of harvesting the nice yummy tomatoes right next to the food bin...
Edited to add: Plus, that doesn't help the issue that when they're waiting for the crops to grow, all they're doing is watering, watering, watering, instead of fishing - as I said, I haven't overfished yet. I shouldn't have to babysit them THAT much that they can't even gather food on their own. Isn't that the point of setting their preference so that they can do these sorts of things when you're not there? Right now I have to make sure I set it to 1/2 speed overnight just so I know there will still be food there when I wake up.