Funny that I should see this today - I am currently having problems with my iPhone 4s battery (about 15 months old), so I think that this thread is a reasonable place to ask a specific question. Especially since we seem to have a battery expert on hand.
My problem is that my phone shuts off with a some of battery remaining. I understand that the percentage shown is an estimate, but quite often it is shutting off at 15%, and this morning it shut off at 27%. Admittedly, I hadn't known about the "30% rule" that was mentioned here, but I usually don't let my phone go all the way down to zero before charging. At least I didn't before it started dying at 15+%.
The interesting part, however, is that if I wait a few minutes and start the phone up again, it boots up and shows the same percentage that it was at before it died. It then operates normally until it either dies properly, or it is recharged. It is almost as if the battery isn't actually dead, but the phone thinks it is.
I have tried a couple of full discharges and recharges for calibration with no improvement. I have also tried restoring my phone, also with no luck. I restored from a backup, however, and not completely "as a new phone."
My latest attempt, after some reading online, was to reset all settings. It is currently charging fully and I guess I'll wait and see if that makes a difference. My last resort, prior to taking it in to Apple, will be to do another full restore, but this time setting it up as a completely new phone.
The one year warranty is over, but I believe that Apple can/will replace the battery if necessary for $80 or so, which is fine. But perhaps someone has some tips before it gets to that. I fee that I have treated my battery fairly well, but I will admit to letting it drain below the 30% threshold more than I should have.