Schmid's cohomological conjecture for non-regular p-groups

Let $p$ be a prime, let $G$ be a finite non-regular $p$-group, and let $\Phi(G)$ denote its Frattini subgroup. Write $Z(\Phi(G))$ for the center of $\Phi(G)$, viewed as a module for $G/\Phi(G)$ under the conjugation action. Let $H^n(G/\Phi(G),Z(\Phi(G)))$ denote the corresponding Tate cohomology group.

Schmid's cohomological conjecture. For every integer $n$, one has

$$H^n\big(\frac{G}{\Phi(G)},Z(\Phi(G))\big)\not=0.$$

Schmid's conjecture concerns the cohomological property used in approaches to the noninner automorphism conjecture. The supplied text does not state whether it has been resolved, so its status is recorded as open.