Battery voltage fluctuation and occasional no restart

Hello all, I have a 2013 Malibu LT, I bought it of an auction and it appears to have a very irritating issue with the battery going dead. I am familiar with the charging system, but am hoping someone can give me a clue. Here is what happens. I start the car and the charging voltage starts at 14.4 then after 30 seconds starts dropping and ends at 12.5 volts. When this happens, if I stop the car it will not start, however, sometimes it stays at 14.2 and never have a problem starting. The car has never died while driving as it stays at 12.5 volts which is enough to keep it going, but not enough to recharge the battery. The battery holds a charge and I have watched the alternator charge at 14.2 and drop to 12.5 with a volt meter and the car's gauge. All connections are tight and clean, any thoughts? Diode in the alternator, voltage regulator??? Help!