The bark is sweet and like candy so yes the rabbits (and other critters) will continue to munch on it. You can use the expandable plastic tree wrap - it will grow with the tree, or you can get some hardware cloth and form it into a cylinder and stake it securely to the ground - the hardware cloth won't come in contact with the tree and can stay in place for years. There are other materials available - corogated plastic that looks like drain pipe, expanded metal mesh, and more. It's worth a bit of expense and effort to save the trees and keep them healthy.
