Deborah, It would be really bad luck to get two batteries that are defective. Not saying it can't happen, but I battery tester at AutoZone.com or other store will tell.
I have heard of this issue being associated with an alternator electrical short. The alternator will still test fine even with a short. The battery and main fuse box are directly connected to the alternator with constant voltage.
Posted on February 10, 2012