I can think of only a couple of possible mends. Put duct tape on the bottom to keep it in place and continute to use it. OR Try to run a small bead of crazy glue along the edge of the tear and quickly push the piece back in place and wait for it to dry. I would still reinforce the bottom with duct tape too. If you decide to crazy glue, make sure to cover the surface you are working on with plastic in case it leaks to the bottom and sticks. Maybe someone else will know of a better solution?