Aleppo soap lasts longest when it can dry out between uses. The bar itself does not need special treatment; what matters most is where it sits after you have used it.
After each use
Rinse the lather off and place the bar where water can drain away, such as a slatted or draining soap dish. A bar left in a puddle softens on the outside and wears down faster.
Between uses
Keep the bar out of the direct stream of the shower or tap. A shelf or ledge a little away from the water lets it dry in the air between washes.
Storing spare bars
Keep spare bars somewhere dry, at room temperature, until you need them. There is no need to wrap them tightly; airflow is fine.
How long a bar lasts
This varies with how often the bar is used and how it is stored. A bar that dries between uses will last longer than one kept wet, but there is no single lifespan for every household.
Related reading: how to use Aleppo soap and make a bar last longer and why Aleppo soap is cured for months.