Let $X$ be a topological space, and $\mathcal{O}_X$ a sheaf of simplicial commutative rings on $X$ such that $(X, \pi_0\mathcal{O}_X)$ is a scheme. Is then in general for $n>0$, the presheaf $\pi_n \mathcal{O}_X$ also a sheaf on $X$? If not, do you have a counterexample?
This is what I've tried so far: if $U \subset X$ is open, and $\{U_i\}$ an open cover of $U$, then for a compatible family $\sigma_i$ in the $\pi_n\mathcal{O}_X(U_i)$, by the Dold-Kan correspondence, we can take representatives $f_i$ in the kernel of the differentials \begin{align} \partial = \sum_k (-1)^k d_k: \mathcal{O}_X(U_i)_n \to \mathcal{O}_X(U_i)_{n-1} \end{align} such that in $\mathcal{O}_X(U_{ij})_n$ it holds \begin{align} f_i |_{U_{ij}} - f_j | _{U_{ij}} = \partial(h_{ij}) \end{align} for certain $h_{ij} \in \mathcal{O}_X(U_{ij})_{n+1}$. But I don't see how I can use this to augment the $f_i$ to a compatible family in the $\mathcal{O}_X(U_i)_n$.
On the other hand, the category of shevaes of simplicial commutative rings on $X$ is equivalent to the category of simplicial objects in sheaves of rings on $X$. Since we know that there are chain complexes of sheaves of abelian groups for which the homology groups are not all sheaves, by the Dold-Kan correspondence, this suggests there might be a counterexample.
Any help is appreciated.