Indian fry bread tastes best hot and fresh out of the frying oil. After 30 minutes or so, it starts losing its structural quality, not unlike French fries. Grilled fry bread lasts a little longer but stiffens after about an hour, like regular bread does.
To keep fry bread fresh while serving, stack the pieces on a paper-towel-lined plate after draining them and cover them with a towel.
For long-term storage, go with the freezer; bread goes stale faster in the refrigerator than at room temperature. At refrigerator temperatures, or around 40 degrees Fahrenheit, the starch molecules in the bread reorder themselves (known as "retrogradation") and crystallize, which creates the firmness synonymous with stale bread.
In the freezer, though, fry bread passes through the crystallization stage so fast it doesn't have time to "go stale," making immediate freezing after cooling the best choice for maintaining freshness.
If you don't want to go the freezer route but want to eek out an extra day or so of relative freshness, wrap the fry bread loosely in plastic wrap or place it in an unsealed food-safe plastic bag and leave it at room temperature.
Freezing Fry Bread
Pat the leftover bread dry with a paper towel after it cools to room temperature and wrap each piece in plastic wrap. Pack the pieces in a heavy-duty freezer bag and store them in the freezer for up to three months (for best taste).
To reheat fry bread, heat the oven to 375 degrees Fahrenheit. Wrap each piece of fry bread in aluminum foil and bake until heated through, about 10 to 12 minutes.
Freezing Fry Bread Dough
Fry bread dough, which, like most other flatbreads, consists of flour, water, salt and baking powder, freezes well and suffers no loss of quality while frozen.
To freeze fry-bread dough, portion the prepared dough into 3-inch balls and arrange them on a baking sheet pan lined with parchment paper or wax paper; space the dough at least one-fourth inch apart.
Place the sheet pan in the freezer long enough for the exterior of the dough to freeze solid; you should be able to rap a dough ball with your knuckles without it leaving an impression. Next, wrap each dough ball in plastic wrap and pack them into heavy-duty freezer bags.
To fry or grill frozen fry-bread dough, transfer the dough packages to the refrigerator the night before. Take the bread out of the refrigerator and unwrap them while cold. Next, let the bread reach room temperature and fry or grill according to the recipe.