2003 v6 charging problems

I hope someone can help. I have a 2003 v6 that I just replaced the battery on. After a week it died and had to be jump started. The bettery cable was then disconnected and the car died. Jumped it again and then everything seemed fine. This has happened two or three times. Every time I check the output on the alternator it is around 14 volts. I have disconnected the battery cable with the car running and sometimes it dies and sometimes it stays running. I hate to replace the alternator if its a voltage regulator since the alternator is $200.

thanks,