A LATAM Airlines Brazil Airbus A320-200, registration PR-MAP performing flight JJ-9615 from Santiago (Chile) to Sao Paulo Guarulhos,SP (Brazil), was enroute at FL390 about 70nm east of Cordoba,CD (Argentina) when the crew initiated an emergency descent due to the loss of cabin pressure and indication the cabin pressure safety valve had opened. The aircraft levelled off at FL100, turned around and diverted to Cordoba for a safe landing on runway 18 about 25 minutes after leaving FL390, the passenger oxygen masks had not been released. Following the replacement of the valve the aircraft was able to continue the flight the following day and reached Sao Paulo with a delay of 20.5 hours.