Thin films of an asymmetric diblock copolymer poly(styrene-block-N-isopropylacrylamide) (P(S-b-NIPAM)) with a long PS and a short PNIPAM block prepared out of a solvent which is more equal in interaction with both blocks than with water allow for water storage without significant swelling of the film. In subsequent storage and removal cycles, the aging of these P(S-b-NIPAM) films is investigated with atomic force microscopy, grazing incidence small-angle X-ray scattering, and in-situ neutron reflectivity. The P(S-b-NIPAM) films are exposed to an atmosphere of deuterated water vapor. Enrichment of the incorporated water in the film part close to the substrate interface is found, The storage capacity decreases by a factor of 2 after seven cycles, but the strongest decrease occurs in the first four cycles. This aging is discussed in the framework of an internal rearrangement of the film structure, H-D exchange, and a possible incorporation of bound water.