Bread made from flour, water, salt and a starter has no preservatives in it, which is the point and also the catch. It will not sit on a counter for ten days pretending to be fresh. Handled well, though, a good loaf gives you most of a week.
Cut side down, no bag
For the first two or three days, keep the loaf out, cut side flat against a board or the counter. The crust is doing the work — it is the wrapper. A plastic bag traps moisture against it and turns a crackling crust soft and leathery overnight.
A linen cloth over the top is fine. A paper bag is fine. Plastic is the enemy of crust — with one exception. A poly bag is excellent if you are re-heating or re-baking the loaf. It is why we like a par-baked loaf: more moisture stays inside, and worked from the freezer in a poly bag it comes out about as good as when it left the oven.
Do not refrigerate
The fridge is the fastest way to stale bread. Starch retrogrades quickest just above freezing, so a refrigerated loaf goes dry and chalky faster than one left out. If you take one thing from this, take that. Refrigerators and microwaves. Ugh.
Freeze early, not late
If you know you will not finish it, slice the loaf and freeze it on day one while it is still at its best. Frozen at its peak, it comes back close to its peak. Frozen on day four, it comes back as day-four bread.
Loaves bagged in poly and frozen keep for weeks, if not months. Toast straight from frozen; no need to thaw. A big, thick loaf is better thawed first, then baked hot and fast — around 400°F for five or six minutes, a little longer if it is large. A cold oven and a long bake gets you a very handsome crouton, not a loaf of bread.
And when it does go hard
Stale sourdough is not waste, it is an ingredient. It is where croutons come from, and bread pudding, and the thick slice that gets fried in butter and topped with an egg. Some of the best things in a Basque kitchen exist because somebody refused to throw bread away. Four-day-old sourdough makes great French toast.