The best insulation to keep ice from melting is a vacuum, which is a volume without any matter in it. Without molecules to propagate heat transfer, vacuum-insulated ice stays cold longer than with any other insulator.
On Earth, the main method by which heat is transferred is conduction. The molecular vibrations of solids, liquids and air, even those of insulating foam, move heat from hot objects to cold objects. The only way to remove the effects of conductive heat transfer is to remove the conductor, which is matter itself. Therefore, major manufacturers of insulators, including the Thermos company, feature products that place a layer of vacuum between the object to be kept cold and the environment.
Even without conductive heat transfer, radiative heat transfer still occurs. All objects above absolute zero radiate heat. To reduce this, the walls of the vacuum chamber are normally coated with a reflective surface, causing most of this radiation to return to its source.
However, even with reflective surfaces and vacuum protecting it, ice cannot stay cold indefinitely if the ambient temperature is above freezing. Enough radiative heat, and conductive heat from the anchors connecting the vacuum chamber to the outer container, eventually gets through to melt the ice.