I agree with your reluctance on sending off your phone. Refurbished will be some "not new" phone you will get back to replace your new one you paid good money for. Most likely won't fix the issue. I read a couple posts now where people sent off their phones for the same reason, only to be out money, with a now refurbished phone.. but with the same problem.
The more I read online about it.. the more I think it's a battery regulator problem. Because my power drops while plugged in and I'm using phone, and that's never happened before.. ever. I believe the battery should "disconnect" and phone run off wall power (which is why phone is always able to charge so fast.. or used to). Probably wrong.. but I'm still trying to find out exactly if the software link can screw with it more (they are already bad.. google iPhone battery regulator) maybe someone with an understanding of the software can better answer if that's possible.
But.. long story short, I'd just try to be patient and see if some fix comes out soon, rather than send off your phone (unless you dropped, soaked, used it as a hammer, played frisbee with it) it's probably not a bad battery or damage.
Until then.. (and I hate to be repetitive) these things extended my battery life .. (BARELY) did NOT fix it
Turn off location services only on "while using"
Turn off background app refresh
Under mail settings - use "fetch" hourly or more
Turn off "automatic updates and downloads" for apps and music..
Yeah I know, it seems like you're taking all the conveniences out of your "smart" phone.. making it a lifeless brick that blinds you every morning when you look at the screen. (Oh yeah, dim your brightness as low as comfortable for you) it might all help a little.
I swear some days my phone is normal.. then others it's a battery hog. I've found I use my phone less.. but always stare at my battery percentage.. hoping it'll be like before.
But.. as I type this.. plugged into a wall.. I've lost 3% (and I'm a fast typer)