We derive a stability criterion for the large-scale structuring of ionospheric plasma clouds due to the E¿B gradient drift instability. For the equilibrium we consider a cylindrical two-dimensional water bag cloud aligned along a uniform magnetic field that is polarized by a uniform neutral wind. We perform a stability analysis that allows three-dimensional perturbations (in r, &thgr;, and z), and we consider both local and global modes. We find that when the parallel wave number kz exceeds a threshold value, exponentially growing poloidal eigenmodes form which are localized on the ''backside'' of the cloud. This is in contrast to the kz=0 limit in which there are no exponential solutions. As kz is increased further, the unstable modes localize at a finite angle away from the backside, at a point where the diamagnetic propagation velocity Vd balances the convective flow velocity of the backgound plasma around the cloud. Vb. We find that the E¿B gradient drift instability is stable when Vd>Vb so that the cloud is no longer susceptible to large-scale structuring. We apply these results to ionospheric barium clouds and estimate that they will cease structuring when L⊥<(cT/eB)(M+2)/2Vn where L⊥ is the transverse size of the cloud. T=Te+Ti is the total temperature, M=nc/nb (nc is the cloud density, and nb is the background density), and Vn is the neutral wind velocity. For mid-latitude barium releases at~180 km we estimate L⊥~160-480 m. which is consistent with observations.