Hello all....I know this is an old post but I too had this very same problem and found a solution that works to what was causing the problem for me....
PROBLEM:
I remember when I first got the phone I charged it to 100% and then used it for the day but it only was at 38% by the end of the day..I would stick it back on the charger...it would charge to 100% and I would leave it charging till next morning....Then at work I would use it for a while and it would get down to 70% by lunch and I would stick it back on the charger to bring it back to 100%....I kept doing this for about 2 weeks and then noticed that when I would use it at home and watch netflix or something that drained the battery quickly it would die at 41%...I would charge it back up and it would come up at the same percentage that it died at....this kept happened but at random percentages...but it would never go down to 1%...I then started noticing that when it charges back to 100% it does not go to 99% or lower for at least an hour of heavy usage when usually it is supposed to start dropping only after 5 or 10 mins or less of usage...I did some research online too and read someones blog that the batteries have built in memory so whatever percentage you are at when you charge your phone back up, is where you phone thinks you are "out of battery"....and in turn will die out when you reach that percentage...Which also explains why it stays at 100% for an hour...the battery is probably looking at the 41% as 0% and therefore it stays at 100% for an hour because it was actually dropping percentage in the battery memory and by the time it dropped to 99% the actual percentage is 58% full....We see 99% full battery on the phone but the actual battery percentage is 58% full....So it dies at what we see as 41% but the actual battery percentage is 0%....
SOLUTION:
You need to let your phone charge all the way to 100% (do not use it at all during this time) and then once it gets to 100% unplug it right away and do not let it "overcharge". Then you must use your phone all the way down till it gets to 1% or even let it die off. Then recharge to full capacity and use till it gets to 1%. It took me a while because the battery was all whacked. I had to charge it to 100%, unplug right away, then let it die off...it would still dies at 41%, then 30% then at 17% and then lower to 8% and then eventually I got it down to 1%....Key is to not charge during the day when the phone still has battery power...wait till it gets down to 1%...
I have been successful doing it this way and now my phone does not die out till it gets to 1%.....except one night when I was ready to go to bed but my phone had 7% left on it...I did not want it to die on me because i use it as my alarm clock so I just charged it at the 7%....I used my phone the next day all the way and when it got to 7% it died on me....that was the first time that had happened in months since I started doing it the new way....I charged it back up fully used it again the next day and it dropped back down to 1% again....so I was glad it did not start acting up and proves the theory of the battery memory.....
Just make sure you do not keep charging your phone back to 100% until you have drained the battery to 1% or completely dead.....
I hope this post helps a lot of people out there...I know I would have been grateful to come across a post like this....GOOD LUCK ALL!!!