Stable non-nullity conjecture for quasitoric manifolds

Let $M$ be a quasitoric manifold, and let $\pi$ denote the canonical map associated with $M$.

Stable non-nullity conjecture. For any quasitoric manifold $M$, $\Sigma^\infty\pi$ is not null homotopic.

This conjecture is motivated by the preceding results, which establish the non-nullity for quasitoric manifolds in several low-dimensional cases, including 4-dimensional manifolds and manifolds over the 3-cube. The general case remains open.