The battery will drag the voltage of the alternator down a little bit as it charges the battery up. I noticed this as I charged mine up after jump starting it when flat and then running the car and monitoring the voltage from my built in voltmeter. It gradually climbs as the battery charge increases. Mine took about 30 mins to creep up from 13volts to 13.9 volts while driving, It could be that your battery has seen better days. Also remember that running the heater fan will drop the battery charge a little, as will lights, rear windown heater if you have one etc. Switch all these off to get a true reading of your battery.