Conservation of particle number in the number-operator approximation of Otsuka and Arima is shown to require a particular normalization for the pair-creation operator. Even with this normalization, two difficulties arise: (a) the average number of particles in a shell can easily violate the Pauli principle, and (b) the mean square fluctuation of the particle number can be negative. As a consequence of the tendency to Pauli violation, the approximate ground-state expectation of the single-particle energy per particle is too low and fails to increase with the number of particles.