Visual information that is relevant for an observer gains prioritized access to awareness (Gayet, Van der Stigchel, & Paffen, 2014). Here we investigate whether information that was relevant for an extended duration is prioritized for access to awareness when it is no longer relevant. We applied a perceptual-learning paradigm, in which observers were trained for 3 days on a speed-discrimination task. This task used a stimulus consisting of two motion directions, of which one was relevant to the task and one irrelevant. Before and after training, we applied a motion-coherence task to validate whether perceptual learning took place, and a breaking continuous flash-suppression (b-CFS) paradigm to assess how training affected access to awareness. The results reveal that motion-coherence thresholds for the task-relevant motion direction selectively decreased after compared to before training, revealing that task-relevant perceptual learning took place. The results of the b-CFS task, however, reveal that access to awareness was not affected by task-relevant learning: Instead, detection times for motion undergoing CFS decreased, irrespective of its direction, after compared to before training. A follow-up experiment showed that the time to detect visual motion also decreased after 3 days without training, revealing that perceptual learning did not cause the general decrease in detection times. The latter is in line with results by Mastropasqua, Tse, and Turatto (2015) and has important consequences for studies applying b-CFS to assess access to awareness: Studies that intend to apply measurements involving b-CFS on different testing days should consider that breakthrough times will dramatically decrease from pre- to postmeasurement.