Can decaying particles raise the upperbound on the Peccei-Quinn scale?

We reexamine the effect of entropy production on the cosmic axion density and find that the Peccei-Quinn scale Fa larger than about 1015 GeV is not allowed even if large entropy is produced by the decays of coherent oscillations or non-relativistic massive particles. We also argue that the Polonyi field in supergravity models is a natural candidate for an entropy-producing source.