On a trivial level it might be that the rate of change of $N$ may not follow such a relationship because (a) there are multiple decay routes, (b) another process/decay is producing $N$ at the same time.
A less trivial point is that the relationship may only be strictly true in a vacuum. For instance, if we take the example of beta decay, the electron that is produced must occupy a quantum energy/momentum state according to the total energy it has after the decay. If this state is already occupied then the Pauli Exclusion Principle would forbid that particular channel.
Of course the decay probability is actually an integral over all possible states, but nevertheless, if a nucleus is surrounded by a degenerate electron gas, then it may not be possible to beta decay if the electron Fermi energy is high enough.
This situation pertains in the crusts and interiors of neutron stars, where the degenerate free electrons have Fermi energies of tens to hundreds of MeV. This results in the presence of very massive, neutron-rich nuclei (in the crust) and a fluid composed mostly of neutrons (in the interior), because the beta decay process is highly suppressed.