We used integral field spectroscopy from CALIFA DR3 and multiwavelength publicly available data to investigate the star formation histories of galaxies in the Seyfert’s Sextet (SS; HCG 79). The galaxies H79a, H79b, H79c, and H79f have low star formation rates despite showing strong signs of interaction. By exploring their individual specific star formation histories, we identified three earlier episodes of strong star formation common to these four galaxies. We use the last two episodes as markers of the epochs when the galaxies were crossing. We suggest that after the first turnaround, initially gas-rich galaxies crossed for the first time, consuming most of their gas. Hence, after the second turnaround most mergers from second crossings would be mixed or dry. The exception would be gas-rich galaxies intruding for the first time. Therefore, we suggest that SS galaxies have survived one crossing during a Hubble time. Strong Balmer absorption lines and the presence of counter-rotating disks provide independent bounds to the second and first crossing, respectively. This scenario provides a plausible way out of the short crossing time paradox.