  We show, for each $q$-continued fraction $G(q)$ in a certain class of
continued fractions, that there is an uncountable set of points on the unit
circle at which $G(q)$ diverges in the general sense. This class includes the
Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued
fraction. We discuss the implications of our theorems for the general
convergence of other $q$-continued fractions, for example the
G\"{o}llnitz-Gordon continued fraction, on the unit circle.
