Stored properly, incense sticks may keep their scent for a few years or even longer. Since the sticks contain essential oils or fragrance oils, storing them in plastic bags is not a good idea, as the chemicals in the oils and plastic affect one another. Instead, store them in wax paper, craft paper or a cotton fabric wrapping.
Incense sticks are usually made from bamboo sticks coated in a mixture of charcoal, resins and powders that acts as a binding agent to hold the fragrance. Some incense from India is made from dry powdered fragrances, while most incense contains an oil-based fragrance. Quality incense is typically scented with essential oils, while cheap dollar-store brands may get their scents from inexpensive fragrance oils.
No matter what type or scent of incense sticks you own, they should be stored in a cool, dry place out of direct sunlight and away from heat sources such as the stove or a heater. Wax paper, thick paper and rice paper all help the sticks maintain their fragrance, although paper wrapping may absorb some of the scented oils from time to time. With quality incense, the original packaging is often designed to keep the incense in good shape. If the incense is in a plastic bag -- nothing between the incense and plastic -- remove the sticks from the bag and wrap them in wax paper or regular paper. A cotton fabric scrap, wrapped roll-style around the scented portion of the incense sticks to form a large roll, also keeps the incense smelling fresh. You'll have a nicely scented piece of fabric afterwards that you can use to scent the inside of dresser drawers. If the cloth looks oily, avoid placing it directly upon finished wood or clothing that may be stained by oil. Staining is unlikely, but it's better to be safe. Store paper- or fabric-wrapped incense sticks in a cardboard or wood box to protect them from breakage and to help maintain their scents.