We present two findings: (i) in the absence of compressibility of (cold) neutrals, the instability triggered by neutral drift due to gradients in plasma density and magnetic field and (ii) the equilibrium pressure-gradient- (PG-) driven instabilities with and without neutral dynamics. The results of detailed analysis suggest that on account of neutral dynamics the growth of these instabilities is suppressed by a neutral perturbational effect. Suppression of PG-driven instabilities is highlighted and the critical wavelength for sustainable growth is found. The physics involved in the mechanism of instabilities is discussed. The endeavour in these investigations is justifiable in its usefulness for understanding the phenomena pertinent to partially ionized plasma (PIP). The stability analysis presented here may be useful for understanding the plasma processes in ‘deep’ coma (very near to the nucleus of coma), at the edges of a plasma column, near a divertor region and in the case of sublimating gas from a cloud.