Temporal attention enhances the perceptual representation of a stimulus at a particular point in time. The number of possible attentional episodes in a given period is limited, but whether observers' confidence reflects such limitations is still unclear. To investigate this issue, we adapted an "Attentional Blink" paradigm, presenting observers with a rapid visual stream of letters containing two targets cued for subsequent perceptual reports and confidence judgments. We found three main results. First, when two targets fell within the same attentional episode, the second target underwent a strong under-confidence bias. In other words, confidence neglected that a single attentional episode can benefit to both targets. Second, despite this initial bias, confidence was strongly correlated with response probability. Third, as confidence was yoked to the evidence used in perceptual reports, it remains blind to delays in response selection for the second target. Notably, the second target was often mistaken with a later item associated with higher confidence. These results suggest that confidence does not perfectly evaluate the limits of temporal attention in challenging situations.