Stable cohomology conjecture for finite p-groups

Let $G$ be a finite $p$-group, and let $d$ be its stable cohomological dimension, namely the largest degree in which stable cohomology of $G$ is nonzero.

Stable-cohomology top-degree conjecture. There exists a $G$-module $A$ with trivial action such that

$$H^d_{\mathrm{s}}(G,A)\neq 0.$$

This asserts that the stable cohomological dimension of every finite $p$-group is attained using a trivial-coefficient module. The source provides no evidence of resolution, so the conjecture remains open.