Cryonic suspension is a method of stabilizing the condition of someone who is terminally ill so that they can be transported to the medical care facilities that will be available in the late 21st or 22nd century. There is little dispute that the condition of a person stored at the temperature of liquid nitrogen is stable, but the process of freezing inflicts a level of damage which cannot be reversed by current medical technology. Could this damage be reversed by future technology? We consider the limits of what medical technology should eventually be able to achieve (based on currently understood chemistry and physics) and whether the repair of frozen tissue is within those limits.