2001 Saturn L200 Car dies while in motion or when slowing d

Have a '01 Saturn L200. Recently car began dying while stopped at a stop sign or a red stop light. Local O'Reilly's confirmed battery needed to be replaced. Replaced battery, still having issues. Car dies when slowing down to stop at a red light or a stop sign. Car will not re-start immediately. Car does a cold start fine and drives approximately 5-7 miles fine before this issue occurs. In last instance, car drove to AND through 4 stop lights, and 2 stop signs before finaling dying on approach to 5 stop light.