  In a previous paper, we showed the existence of an uncountable set of points
on the unit circle at which the Rogers-Ramanujan continued fraction does not
converge to a finite value. In this present paper, we generalise this result to
a wider class of $q$-continued fractions, a class which includes the
Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued
fractions. We show, for each $q$-continued fraction, $G(q)$, in this class,
that there is an uncountable set of points, $Y_{G}$, on the unit circle such
that if $y \in Y_{G}$ then $G(y)$ does not converge to a finite value. We
discuss the implications of our theorems for the convergence of other
$q$-continued fractions, for example the G\"ollnitz-Gordon continued fraction,
on the unit circle.
