We consider a critical superprocess $\{X;\mathbf P_μ\}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index $γ_0 > 1$. We first show that, under some conditions, $\mathbf P_μ(\|X_t\|\neq 0)$ converges to $0$ as $t\to \infty$ and is regularly varying with index $(γ_0-1)^{-1}$. Then we show that, for a large class of non-negative testing functions $f$, the distribution of $\{X_t(f);\mathbf P_μ(\cdot|\|X_t\|\neq 0)\}$, after appropriate rescaling, converges weakly to a positive random variable $\mathbf z^{(γ_0-1)}$ with Laplace transform $E[e^{-u\mathbf z^{(γ_0-1)}}]=1-(1+u^{-(γ_0-1)})^{-1/(γ_0-1)}.$