  We build on our recent results on the Lipschitz dependence of the extreme
spectral values of one-parameter families of pseudodifferential operators with
symbols in a weighted Sj\"ostrand class. We prove that larger symbol classes
lead to H\"older continuity with respect to the parameter. This result is then
used to investigate the behavior of frame bounds of families of Gabor systems
$\mathcal{G}(g,\alpha\Lambda)$ with respect to the parameter $\alpha>0$, where
$\Lambda$ is a set of non-uniform, relatively separated time-frequency shifts,
and $g\in M^1_s(\mathbb{R}^d)$, $0\leq s\leq 2$. In particular, we show that
the frame bounds depend continuously on $\alpha$ if $g\in M^1(\mathbb{R}^d)$,
and are H\"older continuous if $g\in M^1_s(\mathbb{R}^d)$, $0<s\leq 2$, with
the H\"older exponent explicitly given.
