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On the order of magnitude of Sudler products II

We study the asymptotic behavior of Sudler products $P_N(α)= \prod_{r=1}^{N}2|\sin πrα|$ for quadratic irrationals $α\in \mathbb{R}$. In particular, we verify the convergence of certain perturbed Sudler products along subsequences, and show that $\liminf_N P_N(α) = 0$ and $\limsup_N P_N(α)/N = \infty$ whenever the maximal digit in the continued fraction expansion of $α$ exceeds $23$. This generalizes results obtained for the period one case $α=[0; \overline{a}]$.