Has anyone with battery plummet problems been successful in getting AT&T to allow exchange for another phone model after 14 day period?

I've had this phone for about 2 months and tried all sorts of different things to deal with the plummet issue. I've called customer service, tech support, warranty/exchange. New battery X 2, factory reset X 2, replacement GS3. I can sort of deal with it at home with a soft reset. When I'm outside my home in the general vicinity doing something, e.g. running errands near my home, it appears that the battery plummet may occur. I noted this a few times. It is inconvenient to keep checking the battery percentage and soft resetting. I can be occupied doing something and the next thing I know, my battery is drained.

I like the phone, but this issue really is a pain. I know it's a long shot, as AT&T will probably tell me tough luck. I'm not good at raising hell. I'm one of those nice guys that finish last.