Keeping ice frozen when the temperature rises can be a difficult task, particularly if you don't have access to a working freezer. Properly insulating ice, however, can keep it frozen. Different materials will keep ice frozen for different periods of time.
One of the oldest ways to insulate ice is to coat it with layers of sawdust. This method was used in ice houses and even in ice boxes as recently as the early 1900s. Ice that was brought into an ice house during the winter months could be kept cold and insulated well into the summer by making sure it was laid aside and properly coated with sawdust. A sheet or some other material would be placed between the ice and the sawdust, so that the ice could still be used to keep food and drink cold without contamination.
Styrofoam, or polystyrene as this type of plastic is called, also does a good job insulating ice. Developed during the scientific advances made during World War II, polystyrene is a light plastic material that doesn't transfer heat very easily. That means that if ice is kept in a polystyrene container (such as a cooler), the heat from the outside of the container isn't easily transferred to the ice on the inside of the container. That allows the ice to stay away from the heat for longer periods of time, and thus to stay frozen longer.
Surprising as it may sound, air is also a good insulator for ice. That doesn't mean that you should leave ice totally exposed to the elements, though. What it means is that if you trap cold air into a container in a way that it surrounds the ice (such as using a pressurised, plastic container that can be filled with air), it will provide a secondary layer of insulation around the ice. Then heat will not only have to penetrate the outer layer of material (whatever the container is made of) but also the air inside the container. This approach works best in air tight containers such as those used to contain medical supplies.