In this paper, the second of a series of two presenting a detailed description of thermal diffusion cloud chamber operation, we address the operational stability of the vapor-gas mixture in a diffusion cloud chamber with respect to density profile extrema and the accompanying possibility of buoyancy-driven convective flow disturbances. We examine conditions for stable operation (no convective flow disturbances) in the central portion of the cloud chamber, as well as conditions necessary for stable operation in the vicinity of the cloud chamber wall. We find that the total density profile in the central portion of the cloud chamber can pass through a density minimum ever though the density at the upper plate surface is less than the density at the lower plate surface. This local density profile inversion can result in unstable (convective) behavior that propagates through the cloud chamber. Furthermore, we find that local extrema in the total density profile near the chamber wall can lead to subtle, convective flows that are difficult to detect yet can exert a profound influence on nucleation in the central portion of the cloud chamber. We have developed a simple method to estimate the limiting total pressure in a cloud chamber that will support stable operation. From results of our investigations based upon this method, it appears that the thermal diffusion cloud chamber is best suited for experiments at higher temperatures where the accessible total pressure range is largest. Finally, we find that results of our investigation into the effects of total pressure and kind of background gas on nucleation in diffusion cloud chambers involving the low molecular weight alcohols and hydrogen and helium background gases cannot be explained on the basis of these kind of density disturbances occurring within the diffusion cloud chamber. Also, for (relatively) low vapor pressure materials such as 1-pentanol or other high molecular weight alcohols and alkanes stability limitations may preclude nucleation measurements at low temperatures using a diffusion cloud chamber altogether.