Software projects are regularly updated with new functionality and bug fixes through so-called releases. In recent years, many software projects have been shifting to shorter release cycles and this can affect the bug handling activity. Past research has focused on the impact of switching from traditional to rapid release cycles with respect to bug handling activity, but the effect of the rapid release cycle duration has not yet been studied. We empirically investigate releases of 420 open source projects with rapid release cycles to understand the effect of variable and rapid release cycle durations on bug handling activity. We group the releases of these projects into five categories of release cycle durations. For each project, we investigate how the sequence of releases is related to bug handling activity metrics and we study the effect of the variability of cycle durations on bug fixing. Our results did not reveal any statistically significant difference for the studied bug handling activity metrics in the presence of variable rapid release cycle durations. This suggests that the duration of fast release cycles does not seem to impact bug handling activity.