IPhone 4s Battery thinks it's dead when it isn't

Question

I've had my iPhone 4s for almost a year and it's been great. Today it has shut off on me twice and told me that the battery was dead. When I plugged it in to charge it both times it turned back on right away and said it still had more than 3/4 of the battery left. The last time I updated it was whenever the iOs 6.01 came out, I believe a month or two ago and I had no problems then. Last week it could go 2 or 3 days before dying on me and then all of a sudden today it's freaking out. Anybody else had this happen or know how to make it stop happening?

Answer 1

First, try to reset the phone by holding the sleep and homebutton for about 10sec, until the Apple logo comes back again. You will not lose data by resetting.
If this does not work, try to set it up as new device:
How to back up your data and set up as a new device
If still no luck, get your battery checked by Apple, your battery has one year warranty:
iPhone Owners
Your one-year warranty includes replacement coverage for a defective battery. You can extend your coverage to two years from the date of your iPhone purchase with the AppleCare Protection Plan for iPhone. During the plan’s coverage period, Apple will replace the battery if it drops below 50% of its original capacity. If it is out of warranty, Apple offers a battery replacement for $79, plus $6.95 shipping, subject to local tax. Apple disposes of your battery in an environmentally friendly manner