  We prove that, for totally irregular measures $\mu$ on $\mathbb{R}^{d}$ with
$d\geq3$, the $(d-1)$-dimensional Riesz transform $$ T_{A,\mu}^{V}f(x) =
\int_{\mathbb{R}^d} \nabla_{1}\mathcal{E}_{A}^{V}(x,y) f(y) \, d \mu(y) $$
adapted to the Schr\"{o}dinger operator $L_{A}^{V} = -\mathrm{div} A \nabla +
V$ with fundamental solution $\mathcal{E}_{A}^{V}$ is not bounded on
$L^{2}(\mu)$. This generalises recent results obtained by Conde-Alonso,
Mourgoglou and Tolsa for free-space elliptic operators with H\"older continuous
coefficients $A$ since it allows for the presence of potentials $V$ in the
reverse H\"{o}lder class $RH_{d}$. We achieve this by obtaining new exponential
decay estimates for the kernel $\nabla_{1} \mathcal{E}_{A}^{V}$ as well as
H\"older regularity estimates at local scales determined by the potential's
critical radius function.
