Glad to hear that your phone is performing normally now! Though I feel like it's quite the coincidence that everyone experiencing this problem would suddenly have failing batteries, considering it seems to be a range of iPhone models, purchase dates, and iOS versions. I mean, just look at the 65+ page thread that ellenfrompalmerton mentioned... it seems like there is some bigger issue here.
I did a quick test on the app Battery Life and apparently my battery is in good condition — only degraded about 6% in capacity since I purchased it 2 years ago. Granted, the numbers from that app may not be accurate to a tee, but I feel like it would have picked up on any serious problems. My coworker suggested recalibrating the battery, and I'm going to see if it helps. It's essentially charging the phone to 100%, letting it drain to 0%, charging it back up to 100% while the phone is turned off, though you can read the step-by-step instructions here if anyone is interested: http://www.appledystopia.com/how-to/calibrate-iphone-battery/