After driving Prius v for few months in the summer I've noticed that Prius v charging system is not adequate, I connected the charger and noticed that the battery was charge was between 25 to 50% level. Yes I do short trips but it shouldn't make any difference. It seems to me the battery has to be charger with an external charger once a week.
If you don't use your car for several days, is battery completely dead? My (old) non-hybrid Camry has this problem. Replaced battery several times, alternator. Maybe test for ghost current draws?
If it set on the dealer lot for a length of time - they probably "killed" the battery letting it run flat 1 too many times... take it back- get a new one under warranty... it may also have a shorted cell causing it not to take a full charge and go flat quickly. try a new one first - I got mine fresh off the boat and delivery truck with 9 mile (pre-delivery inspection) ... so it didn't set in the shop for more then a couple days since it arrived in the states... I haven't had any trouble - driven daily, mon. thru fri. rarely on weekend.