Gum loses its flavor because saliva breaks down and digests the sweeteners that were added to the base. The ingredients are eventually digested completely and only the base of the gum remains.
Gum is made up of a rubber base from the Sapodilla tree called Chicle. The base has no flavoring by itself; gum manufactures add different flavors and sweeteners to give the gum a more enjoyable taste. The sweeteners are made up of different artificial ingredients, such as corn syrup or sugar, that are digested through the saliva. Eventually, all of the artificial ingredients are broken down and sent through the digestive system, which leaves only the tasteless rubber gum base.