I have the same issue as well, now it has become nothing more than a paper weight to listen to music.
Bloody phone needs to be constantly plugged in .
phone calls will last 3-5 mins unless it is plugged in, same for using wifi, data, etc.
I shut down all the apps and still same problem, often enough at 98% power, the phone will shut down, especially if using Safari/wifi, or data.
My phone is all original, I never believed in jail breaking or modifying any of my electronic equipment, I have restored my phone at least 4 times, what a waste of time.
I am lucky enough that my company supplies me a BlackBerry (that I dislike) but at lease I now forward all my calls to my Co. phone, but not everyone has that luxury.
I went to an Apple store, I did not get to see a technician (wayyyy too busy), but I saw a service rep. when I explained the problem, they would hmmm and hawww, and constantly say Yeahh, and finish with Y'know that 3Gs is quite old, you should be upgrading to the 4gs! *** ???? is that your answer. I said since I up graded to 5.1.1 I have developped these problems shortly after the up grade. you can't even down grade back to the earlier version before the upgrade.
Marcus, I think Apple is too big to think of us simple clients, and just don't care. Right now I am really considering the new Samsung Galaxy SIII.
After seeing all the frustrated good folks that have this issue, and seeing how Apple is doing nothing about it really burns me
Frustrated user 😟