Gluten-free bread left on the counter molds within a short period of time, and gluten-free bread stored in the refrigerator dries out with astonishing rapidity. It seems like a losing proposition either way.
However, I have discovered, quite by accident, that putting a portion of a baked potato in the same container with gluten-free bread and storing them together in the refrigerator keeps the bread fresh and moist. I have tried using a piece of raw potato, and it didn't work. Possibly a piece of cut fruit would accomplish the same thing, but a baked potato does not impart flavor to the bread as fruit might do, and although the baked potato shrivels, it does not turn brown and mold as fruit would after several days.
Freezing gluten-free bread is another way to keep it from drying out. I have recently read several methods of freezing gluten-free bread, and they all involve putting some sort of wrap between each slice and double or triple wrapping the bread.
It doesn't have to be that complicated. For loaf bread, I simply slice the entire loaf, stack the pieces in several piles (usually four) in a gallon-size plastic zipper storage bag and lay the sealed bag flat in the freezer. By stacking the bread slices in separate piles, I can remove one stack of slices and transfer it to the refrigerator when I need it, thus thawing only part of the loaf at a time.
When I need bread immediately, I put a stack of frozen slices in the microwave oven for a few seconds, thawing the stack just enough to allow me to pry off one or two slices. Then I finish thawing in the microwave the pieces that I want to eat immediately and put the rest of the stack in a sandwich-size storage bag or container in the refrigerator to thaw gradually.
Muffins can also be stored in the freezer in plastic zipper storage bags and removed one at a time for use.