Non-contractibility conjecture for non-Hamiltonian subcircle actions

Let an $m$-dimensional torus $T$ act symplectically on a $2n$-dimensional closed connected symplectic manifold $(M,\omega)$. Let $2r$ be the rank of the two-form $\omega_T$ from the paper's preceding result, and assume

$$m \ge n+r-1.$$

Non-contractibility conjecture. Then for every non-Hamiltonian subcircle action of $T$, the orbits of the circle action and all of their iterates are non-contractible.

This is proposed as a natural generalization of the paper's complexity-one torsion result to symplectic torus actions with non-isotropic orbits. The source presents it as a belief rather than a result, and gives no resolution, so its status remains open.