Oh, Sega was limping along well before the Saturn's failure let Sony finish them off. They completely fractured their market when they botched both the (expensive to manufacture) 32X and SegaCD, canceled the integrated (cheaper) Neptune, then failed to showcase the Saturn as their next generation while simultaneously making it too hard to develop for.

Even when Dreamcast finally became a clean-slate for Sega, it was far too late to serve as a 5th chance.

Second chance in that the Dreamcast was doing very well in the west, but not in Japan. They elected to kill it because the Japanese side was struggling. I dont think they saw much continued success without them. It was Peter Moore who ultimately made the call to kill the Dreamcast.