  We prove that for the functions of the form $g(x) = h(x) + \frac{C}{x+i}$,
where $h$ belongs to the continuous Wiener algebra $W_0$, the intersection of
the frame set $\mathcal{F}_g$ with every hyperbola $\{\alpha, \beta > 0 \mid
\alpha\beta = c\}$ is open in the relative topology. In particular, this
applies to all rational functions $g$.
