How can I alter these wooden towel hooks so that the towels don't fall off?
Find more twine or rope (looks like a natural sisal) that matches the "laces" on the shoes. Wrap the twine around the posts in a spiral until they are completely covered. You will probably need to glue the twine occasionally, and perhaps rough up the paint so the glue sticks.

The twine in the picture looks like it is waxed. I would make sure to use non-waxed if you are going to wrap the posts, otherwise the towels would still probably slip right off.