  We determine the stability conditions for a radially symmetric noncommutative
scalar soliton at finite noncommutivity parameter $\theta$. We find an
intriguing relationship between the stability and existence conditions for all
level-1 solutions, in that they all have nearly-vanishing stability eigenvalues
at critical $\theta m^2$. The stability or non-stability of the system may then
be determined entirely by the $\phi^3$ coefficient in the potential. For
higher-level solutions we find an ambiguity in extrapolating solutions to
finite $\theta$ which prevents us from making any general statements. For these
stability may be determined by comparing the fluctuation eigenvalues to
critical values which we calculate.
