Battery discharges quickly

2002 mercury Grand Marquis LS, 4.6 liter engine, auto trans, 2 wheel drive, 45 k miles. New battery. Battery and alternator checked at checker auto, alternator was at 13 output. Trunk light disconnected, Light under hood disconnected. Red blinking light on top of dash always on. This car loses all battery response in 48 hours, will not even click or light the radio. Is it possible that the alternator is still the culprit and does not fully charge the battery? If not, what else do I check?