We examine the metallicity and age of a large set of Sloan Digital Sky Survey/Data Release 6 galaxies that may be blue compact dwarf (BCD) galaxies during quiescence (QBCDs). The individual spectra are first classified and then averaged to reduce noise. The metallicity inferred from emission lines (tracing ionized gas) exceeds by ~0.35 dex the metallicity inferred from absorption lines (tracing stars). Such a small difference is significant according to our error budget estimate. The same procedure was applied to a reference sample of BCDs, and in this case the two metallicities agree, being also consistent with the stellar metallicity in QBCDs. Chemical evolution models indicate that the gas metallicity of QBCDs is too high to be representative of the galaxy as a whole, but it can represent a small fraction of the galactic gas, self-enriched by previous starbursts. The luminosity-weighted stellar age of QBCDs spans the whole range between 1 and 10 Gyr, whereas it is always smaller than 1 Gyr for BCDs. Our stellar ages and metallicities rely on a single stellar population spectrum fitting procedure, which we have specifically developed for this work using the stellar library MILES.